Chapter 5, Problem 27RE

Explanation of Solution

Truth table:

p	q	r	!r	$\left(p\&\&q\right)$	$\left(p\&\&q\right)\left|\right|!r$	$!(\left(p\&\&q\right)||!r)$
False	False	False	True	False	True	False
False	False	True	False	False	False	True
False	True	False	True	False	True	False
False	True	True	False	False	False	True
True	False	False	True	False	True	False
True	False	True	False	False	False	True
True	True	False	True	True	True	False
True	True	True	False	True	True	False

AND gate:

• The “AND” gate refers to a logic gate whose output will be “HIGH” only when all the inputs are “HIGH”.
• The output of “AND” gate will be “LOW” when any one of its input will be “LOW”.
• The truth table for “AND” gate is as follows:

p	q	$Y=p\&\&q$
False	False	False
False	True	False
True	False	False
True	True	True

OR gate:

• The “OR” gate refers to a logic gate whose output will be “HIGH” when any one of the inputs or both is “HIGH”