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  • Please,please help me Which one of the following statements is a tautology ?

Which one of the following statements is a tautology ?

  • Option 1)

    p\rightarrow (p\rightarrow q)

  • Option 2)

    (p\vee q)\rightarrow q

  • Option 3)

    p\vee (p\rightarrow q)

  • Option 4)

    p\vee (q\rightarrow p)

 

Answers (1)

As learnt in

Truth table of 'OR' operator -

-

 

 As learnt in

Truth Table of "if-then" -

Figure 4

-

 

 As learnt in

Tautology -

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

-

 

                                      (i)                       (ii)                     (iii)                     (iv)

p q p \rightarrow q q \rightarrow p  p \rightarrow (p\rightarrow q) (p\vee q) \rightarrow q p\vee (p\rightarrow q) p\vee (q\rightarrow p)
T T T T T T T T
T F F T F F T T
F T T F T T T F
F F T T T T T T

So p\vee (p\rightarrow q) is always true, Hence it is a tautology.


Option 1)

p\rightarrow (p\rightarrow q)

This Answer is incorrect.

Option 2)

(p\vee q)\rightarrow q

This Answer is incorrect.

Option 3)

p\vee (p\rightarrow q)

This Answer is correct.

Option 4)

p\vee (q\rightarrow p)

This Answer is incorrect.

Posted by

Vakul

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