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The statement p\rightarrow (q\rightarrow p) is equivalent to

Option: 1

p\rightarrow (p\rightarrow q)
 


Option: 2

p\rightarrow (p\vee q)


Option: 3

p\rightarrow (p\wedge q)

 


Option: 4

p\rightarrow (p\leftrightarrow q)


Answers (1)

best_answer

 

Truth table of 'OR' operator -

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Truth Table of "if-then" -

Figure 4

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Tautology -

A tautology is called a theorem. It only contains T in the last column of its truth table.

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p\rightarrow (q\rightarrow p)\equiv \sim p\vee (q\rightarrow p)

\equiv (\sim p)\vee (\sim q\vee p)

\equiv (\sim q)\vee (p\: \vee \sim p)

\equiv (\sim q)\vee T=T

\therefore p\rightarrow (q\rightarrow p) is a tautology.        

Also p\rightarrow (p\vee q )\equiv\sim p\vee (p\vee q)

\equiv (\sim p\vee p)\vee q\equiv T\vee q=T

\therefore p\rightarrow (p\vee q) is also a tautology.

Thus, p\rightarrow (q\rightarrow p) is equivalent to p\rightarrow (p\vee q)

Posted by

Ritika Jonwal

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