| Statement-1: r is equivalent to either q or p. |
| Statement-2: r is equivalent to \[\sim \left( p\leftrightarrow \,\sim q \right)\]. |
A) Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
B) Statement-1 is true, Statement-2 is false.
C) Statement-1 is false, Statement-2 is true.
D) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Correct Answer: D
Solution :
p : x is an irrational number q : y is a transcendental number r : x is a rational number iff y is a transcendental number \[\Rightarrow \,\,r:\sim p\leftrightarrow \,q\] \[{{s}_{1}}\] : q or p \[{{s}_{2}}:\sim \left( p\leftrightarrow \sim q \right)\]| P | Q | \[\sim p\] | \[\sim q\] | R \[\sim p\leftrightarrow q\] | \[{{s}_{1}}\]q or p | \[p\leftrightarrow \sim q\] | \[{{s}_{2}}\sim \left( p\leftrightarrow \sim q \right)\] |
| T | T | F | F | F | T | F | T |
| T | F | F | T | T | T | T | F |
| F | T | T | F | T | T | T | F |
| F | F | T | T | F | F | F | T |
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