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  • Given the following two statements: <img alt="\left (S_{1} \right ):\left ( q\wedge p \right )\rightarrow (p\leftrightarrow \sim q)" src="http://entrancecorner.codecogs.com/gif.latex?%5Cleft%20%28S_%7B1%7D%20%5Cright%20%29%3A%5Cleft%20%28%20q%5Cwedge%2

Given the following two statements: \left (S_{1} \right ):\left ( q\wedge p \right )\rightarrow (p\leftrightarrow \sim q) is tautology. \left (S_{2} \right ):\sim q\wedge (\sim p\leftrightarrow q) is fallacy. Then :
Option: 1 both (S_{1}) and (S_{2}) are correct
Option: 2 only (S_{1}) is correct
Option: 3 only (S_{2}) is correct
Option: 4 both (S_{1}) and (S_{2}) are not correct

Answers (1)

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Let TV of (r) denotes truth value of a statement r.

\begin{array}{l} \text { Now, if } T V(p)=T V(q)=T \\ \Rightarrow T V\left(S_{1}\right)=F \\ \text { Also, if } T V(p)=T \& T V(q)=F \\ \Rightarrow T V\left(S_{2}\right)=T \end{array}

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