Question

Given the true statements:

(1) If $a$ is greater than $b$, then $c$ is greater than $d$

(2) If $c$ is less than $d$, then $e$ is greater than $f$. A valid conclusion is:

• A. If $a$ is less than $b$, then $e$ is greater than $f$
• B. If $e$ is greater than $f$, then $a$ is less than $b$
• C. If $e$ is less than $f$, then $a$ is greater than $b$
• D. If $a$ is greater than $b$ then $e$ is less than $f$
• E. none of these

Answer 1

Answer: (E)

none of these

Let $p$ be the proposition "a is greater than b".

Let $q$ be the proposition "c is greater than d".

Let $r$ be the proposition "e is greater than f".

From the given problem, $p\to q$ and $\sim q\to r$.

From the rule of Contrapositive , we get,

$\sim q\to \sim p$ and $\sim r\to q$

Therefore a, b, c and d are not valid conclusions.