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
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
- Ap, q and r, s
- Bp, r and q, s
- Correct answerCp, s and q, r
- Dno 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
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'.