Boolean or truthvalued expressions are how we express condit

Boolean or \"truth-valued\" expressions are how we express conditions that control choices and repetition in computer languages. Consider the following Python Boolean expression, where variables beta and gamma are of type Boolean: not (beta and gamma) In any algebraic notation there are usually several different ways of writing the same expression. For instance,in integer arithmetic the value of expression 4 x (5 + 2) is numerically equivalent to that of expression\'(4 x 5)+(4 x 2). Which of the following Boolean expressions is logically equivalent to the one above? (not beta) and (not gamma) (not beta) or (not gamma) beta and (not gamma) not (not beta) or gamma beta or gamma

Solution

As beta & gamma are boolean variables they can b either true(T) or false(F).

We can find the correct option by making the truth table:-

(not beta) and(not gamma)

(not beta)

or(not gamma)

we can see that truth table for given expression not(beta and gamma) is similiar to truth table for option 2.

hence expression similiar to given one is:-

(not beta) or(not gamma) (answer)

  

VARIABLES	given expression	option 1	option 2	option 3	option 4	option 5
beta	gamma	not(beta and gamma)	(not beta) and(not gamma)	(not beta) or(not gamma)	beta and (not gamma)	not (not beta) or gamma	beta or gamma
T	F	T	F	T	T	T	T
T	T	F	F	F	F	T	T
F	T	T	F	T	F	T	T
F	F	T	T	T	F	F	F