Q62 / 150 · MHT CET 2026 (17 April Shift 1) · Mathematics

If the statements
p: If voltage increases then current decreases.
q : If voltage does not increases then current does not decreases.
r : If current decreases then voltage increases.
s : If current does not decreases then voltage does not increases.
then which of the following pairs of statements having same meaning

  • A
    p, q and r, s
  • B
    p, r and q, s
  • Correct answer
    C
    p, s and q, r
  • D
    no pair having same meaning

Solution

Let $V$ be the statement "voltage increases".

Let $C$ be the statement "current decreases".

The given statements can be represented symbolically as:

$p : V \rightarrow C$

$q : \sim V \rightarrow \sim C$

$r : C \rightarrow V$

$s : \sim C \rightarrow \sim V$

A conditional statement is logically equivalent to its contrapositive ($A \rightarrow B \equiv \sim B \rightarrow \sim A$).

The contrapositive of statement $p$ ($V \rightarrow C$) is $\sim C \rightarrow \sim V$, which is exactly statement $s$. Thus, $p$ and $s$ are logically equivalent.

The contrapositive of statement $q$ ($\sim V \rightarrow \sim C$) is $C \rightarrow V$, which is exactly statement $r$. Thus, $q$ and $r$ are logically equivalent.

Therefore, the pairs of statements having the same meaning are $p, s$ and $q, r$.

Answer: p, s and q, r

Hence, the correct answer is option: 'C'.

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