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Mathematical Reasoning
normal
The statment $ \sim \left( {p \leftrightarrow \sim q} \right)$ is
A
Equivalent to $p \leftrightarrow q$
B
'Equivalent to $ \sim p \leftrightarrow q$
C
A tautalogy
D
A fallacy
Solution
| $p$ | $q$ | $ \sim p$ | $ \sim q$ | $p \leftrightarrow \sim q$ | $ \sim \left[ {p \leftrightarrow \sim q} \right]$ | $ \sim \left\{ {p \leftrightarrow q} \right\}$ | ${p \leftrightarrow q}$ |
| $T$ | $T$ | $F$ | $F$ | $F$ | $T$ | $F$ | $T$ |
| $T$ | $F$ | $F$ | $T$ | $T$ | $F$ | $T$ | $F$ |
| $F$ | $T$ | $T$ | $F$ | $T$ | $F$ | $T$ | $F$ |
| $F$ | $F$ | $T$ | $T$ | $F$ | $T$ | $F$ | $T$ |
Clerly $ \sim \left( {p \leftrightarrow \sim q} \right)$ is equivalent to ${p \leftrightarrow q}$
Standard 11
Mathematics
