Question

question: 13
the ap exam uses the following relational (comparison) operators: =, ≠, >, <, ≥, and ≤.
as well, and, or and not are used instead of &&, || and !=.
a comparison using a relational operator evaluates to a boolean value. for example, a = b evaluates to true if a and b are
equal; otherwise, it evaluates to false.
which of the following boolean expressions is equivalent to the expression?
(a and b) or (a and c)
(a and b) or c
(a and b) and (a and c)
(b and c) or a
a and (b or c)

Explanation:

Step1: Apply distributive law

The distributive law for Boolean expressions states that \(x\ AND\ (y\ OR\ z)=(x\ AND\ y)\ OR\ (x\ AND\ z)\). Here, if we let \(x = a\), \(y = b\), and \(z = c\), then \((a\ AND\ b)\ OR\ (a\ AND\ c)=a\ AND\ (b\ OR\ c)\)

Answer:

a AND (b OR c)