Question

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
• C. p, s and q, r
• D. no pair having same meaning

Hint:

A conditional is equivalent to its contrapositive.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Let \(A\): voltage increases, and \(B\): current decreases. Then \(p: A\to B\), \(q: \sim A\to\sim B\), \(r: B\to A\), \(s: \sim B\to\sim A\).

Step 2: Key Formula or Approach
A statement \(X\to Y\) is equivalent to its contrapositive \(\sim Y\to\sim X\).

Step 3: Detailed Explanation
The contrapositive of \(p: A\to B\) is \(\sim B\to\sim A\), which is \(s\). So \(p\) and \(s\) have the same meaning.
The contrapositive of \(r: B\to A\) is \(\sim A\to\sim B\), which is \(q\). So \(q\) and \(r\) have the same meaning.
The pairs are \((p,s)\) and \((q,r)\).

Final Answer:
The equivalent pairs are \(p,s\) and \(q,r\), option (C). \[ \boxed{(p,s)\ \text{and}\ (q,r)\ \text{(C)}} \]