Question

state the truth value of (p and ~p)​

Answer 1

truth value of (p and ~p) is F

p ~p (p and ~p)

T F F

Answer 2

The Truth value of the given expression ( p ^ ~p ) is False i.e. 0 for all values of p.

Bitwise Operators :

• The NOT operator i.e. ~p is also called negation. It negates the value i.e. True to False and vice versa.
• The AND operator i.e. p^q is only satisfied i.e. True when both its conditions i.e. p and q are True. In other cases, it is false.

NOT Operator Truth Table( ~ ) :

p                  ~p

---------------------------

True   (1)      False (0)

False (0)     True   (1)

AND Operator Truth Table( ^ ) :

p                   q                        p^q

--------------------------------------------------

True   (1)       True   (1)       True   (1)

True   (1)       False (0)       False (0)  

False  (0)      True   (1)       False (0)

False  (0)      False (0)       False (0)  

Thus, the required truth table is

Finding Truth Table for ( p ^ ~p ) :

p                   ~p                        p^(~p)

--------------------------------------------------

True   (1)       False (0)       False (0)  

False  (0)      True   (1)       False (0)

Hence, the value of ( p ^ ~p ) is False i.e. 0 for both values of p i.e. True(1) and False(0).

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