Who is the oldest

Logic Level 1

Abdul is younger than Abdullah.
Peg is older than Abdul.
Abdullah is older than Peg.

If the first two statements are true, the third statement is $\text{\_\_\_\_\_\_\_\_\_\_} .$

true false uncertain

3 solutions

Zach Abueg
Jan 8, 2017

Let

Abdul = $A$

Abdullah = $B$

Peg = $C$

It is given that the following are true $:$

$B > A$

$C > A$

Is it true, then, that $B > C?$ Not necessarily $:$ both are greater than $A$ , but we do not know by how much . Thus, it is uncertain as to whether $B$ or $C$ is greater.

To illustrate, let's work with some numbers:

$A = 1, B = 6, C = 5$

then the first two statements hold true, as does the last one $:$

$6 > 1$

$5 > 1$

$6 > 5$

Now let

$A = 1, B = 5, C = 6$

The first two statements still hold true $:$

$5 > 1$

$6 > 1$

But the last, $B > C$ , is no longer true $:$

$5 \ngtr 6$

Thus, Abdullah is not necessarily older than Peg.

A Former Brilliant Member
Jan 5, 2017

Because the first two sentences are true, both Both Abdulah and Peg are older than Abdul. However, it is uncertain as to whether Abdulah is older than Peg

What is the difference between the options of "uncertain" and "sometimes true"?

Calvin Lin Staff - 4 years, 5 months ago

I would guess that "sometimes true" implies that it is sometimes true that Abdullah is older than Peg, and sometimes it isn't true. Uncertain implies that it is always true or false, we just don't know which.

Nick Schreiner - 4 years, 5 months ago

Keerthi Bychapur
Jan 10, 2017

From statements we can say that Abdullah and peg both are elder than Abdul nothing comparison about the ages of Abdullah and peg so it is uncertain.

Who is the oldest

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