Determining Whether a Statement is True, False, or Uncertain - HSPT Language Skills

Let's use symbols from math to help us understand this:

(1) Jeremy is taller than Jean: Jeremy > Jean

(2) John is shorter than Jeremy: John < Jeremy

This could be rewritten: Jeremy > John

Thus, we know that Jeremy is taller than Jean and John; however, we do not know anything about the relationship between John and Jean.

Let’s use symbols from math to help us understand this.

(1) Thomas is smarter than Luca: Thomas > Luca

(2) Luca is smarter than John: Luca > John

We could string these together as well:

Thomas > Luca > John

John is not smarter than Thomas; therefore, this is false.

Let’s use symbols from math to help us understand this.

(1) Baruch is weirder than Frederick: Baruch > Frederick

(2) Frederick is weirder than Arthur: Frederick > Arthur

These can all be combined to give us:

Baruch > Frederick > Arthur

It is indeed the case that (3) Baruch > Arthur.

Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "more known," and "less than" (<) will mean "more unknown."

(1) Godfrey is more unknown than Henry: Godfrey < Henry

This could be rewritten: Henry > Godfrey

(2) Henry is better known than Giles: Henry > Giles

Thus, we know that Henry is more known than both Giles and Godfrey; however, this does not tell us anything about the relationship between Giles and Godfrey. Therefore (3) is uncertain.

Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "has more fun," and "less than" (<) will mean "has less fun."

(1) Teddy has more fun than Jack: Teddy > Jack

(2) Franklin has less fun than Jack: Franklin < Jack

This could also be written: Jack > Franklin

Therefore, we could string all of these together into:

Teddy > Jack > Franklin

Therefore, (3) Teddy > Franklin does hold.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “taller,” and “less than” (<) will mean “shorter.”

(1) Andrew is taller than Abraham: Andrew > Abraham

(2) Abraham is shorter than Charles: Abraham < Charles

This could be rewritten: Charles > Abraham

Another way of looking at these two would be:

(1) Abraham < Andrew

(2) Abraham < Charles

This tells us that Abraham is shorter than Andrew and Charles. It tells us nothing about the relationship between Charles and Andrew.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more difficult,” and “less than” (<) will mean “easier.”

(1) Physics is more difficult than chemistry: Physics > chemistry

This could be rewritten: Chemistry < physics

(2) Chemistry is easier than philosophy: Chemistry < philosophy

Therefore, this tells us that chemistry is easier than the other two subjects. However, it does not tell us anything about the relationship between philosophy and physics.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “harder to drive in,” and “less than” (<) will mean “easier to drive in.”

(1) It is easier to drive in snow than it is in ice: snow < ice

(2) It is harder to drive in snow than in rain: snow > rain

This could be rewritten: rain < snow.

All of these could be combined to give us: rain < snow < ice.

This means that rain is indead easier to drive in that ice.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “runs more quickly,” and “less than” (<) will mean “runs more slowly.”

(1) Robert runs more quickly than Nicole: Robert > Nicole

(2) Nicole runs more quickly than Fred: Nicole > Fred

This could give us a combined statement:

Robert > Nicole > Fred

Now, (3) could be rewritten: Fred < Robert. This is the same thing as Robert > Fred, which we do see above as being true.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more efficient than,” and “less than” (<) will mean “less efficient than.”

(1) Nuclear power is more efficient than coal power: nuclear > coal

This could be rewritten as: coal < nuclear

(2) Coal power is less efficient than gas power: coal < gas

Thus, we are told that coal is less efficient than both nuclear and gas; however, we are told nothing about the relationship between nuclear and gas power.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more on the road,” and “less than” (<) will mean “less on the road.”

(1) There are more cabs than trucks on the roads in New York City: cabs > trucks

This could be rewritten as: trucks < cabs

(2) There are more motorcycles than there are trucks on the roads in New York City: motorcycles > trucks

This could be rewritten as: trucks < motocycles

Thus, we are actually only being told something about trucks—there are fewer of them than both cabs and motorcycles (in New York City). Thus, we cannot say anything about the relationship between the number of cabs and the number of motorcycles.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more frightening,” and “less than” (<) will mean “less frightening.”

(1) Gremlins are more frightening than ogres: gremlins > ogres

(2) Skeletons are less frightening than ogres: skeletons < ogres

This could be rewritten as: ogres > skeletons

All together, we can say:

gremlins > ogres > skeletons

Therefore, it is indeed the case that gremlins are more frightening than skeletons.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “has a greater salary than,” and “less than” (<) will mean “has a lower salary than.”

(1) George has a greater salary than John: George > John

(2) Filbert has a lower salary than George: Filbert < George

This could be rewritten as: George > Filbert

This means that we are being told that George has a greater salary than both John and Filbert; however, it tells us nothing about the relation between these latter two men.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is smarter than.”

(1) Paul is smarter than Peter: Paul > Peter

(2) Peter is smarter than Andrew: Peter > Andrew

These could be combined to give us:

Paul > Peter > Andrew

Therefore, it is false to say that Andrew is smarter than Paul.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is more boring than,” and “less than” (<) will mean “is less boring than.”

(1) Emmanuel is more boring than David: Emmanuel > David

(2) Emmanuel is less boring than John: Emmanuel < John

This could be rewritten: John > Emmanuel

We could thus combine these as: John > Emmanuel > David

Thus it is false to say that David is more boring than John.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more mature,” and “less than” (<) will mean “more immature.”

(1) Children are more immature than adults: children < adults

This could be rewritten: adults > children

(2) Adults are more mature than teenagers: adults > teenagers

Therefore, all that we are being told is that adults are more mature than both teenagers and children. Nothing can be inferred regarding the relative status of teenagers and children.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “braver,” and “less than” (<) will mean “more cowardly (less brave).”

(1) Thomas is braver than Henry: Thomas > Henry

(2) Thomas is more cowardly than Athanasius: Thomas < Athanasius

Note, this could be rewritten: Athansius > Thomas

Thus, we could put together the two statements and get:

Athanasius > Thomas > Henry

Therefore, it is true to say that Athanasius is braver than Henry.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “has a more beautiful tone,” and “less than” (<) will mean “has a less beautiful tone.”

(1) The tuba has a more beautiful tone than the trumpet: tuba > trumpet

(2) The flute has a less beautiful tone than the trumpet: flute < trumpet

This could be rewritten: trumpet > flute

Therefore, we could combine these to get:

tuba > trumpet > flute

Therefore, it is not true to say that the tuba has a less beautiful tone than the flute.

Let’s use symbols from math to help us understand this and treat "wakes" as the opposite of "makes drowsier (i.e. less awake)." “Greater than” (>) will mean “wakes,” and “less than” (<) will mean “makes drowsier.”

(1) Oatmeal wakes Sara better than chocolate does: oatmeal > chocolate

(2) Peanut butter makes Sara drowsier than does chocolate: peanut butter < chocolate

This could be rewritten: chocolate > peanut butter

Note that we could combine all of these into:

oatmeal > chocolate > peanut butter

Thus, oatmeal does indeed wake Sara better than peanut butter.

Some vocabulary is necessary first. "Beneficient" means "giving or generous." (Think of "benefit," which is related to this word). To be "miserly" is to be "stingy," not wishing to give out money or gifts.

Now, let's use symbols from math to help us understand this. “Greater than” (>) will mean “more beneficent,” and “less than” (<) will mean “more miserly (i.e. less beneficent).”

(1) Scott is more beneficent than Michael: Scott > Michael

Note that this could be rewritten: Michael < Scott

(2) Michael is more miserly than Peter: Michael < Peter

Therefore, all that we are being told is that Michael is less beneficent than both of the other men. There is no necessary relationship described about Scott and Peter.