Boolean expression practice exercise 4 solution

Exercise

The following table shows the value of an expression based on the values of a, b, and c.

Value of `a`	Value of `b`	Value of `c`	Value of expression
`true`	`true`	`true`	`false`
`true`	`true`	`false`	`true`
`true`	`false`	`true`	`true`
`true`	`false`	`false`	`true`
`false`	`true`	`true`	`true`
`false`	`true`	`false`	`true`
`false`	`false`	`true`	`true`
`false`	`false`	`false`	`true`

Which of the following expressions are equivalent to the value of the expression shown in the table?

Select TWO answers.

(A) (NOT a) OR (NOT b) OR (NOT c)

(B) NOT (a OR b OR c)

(D) (NOT a) AND (NOT b) AND (NOT c)

(A) (NOT a) OR (NOT b) OR (NOT c)

The expression evaluates to false if and only if a, b, and c are all true.

Write the expression as if it evaluated to true in the above circumstance.

a AND b AND c

Add a NOT to the entire expression to make it false.

NOT (a AND b AND c)

This is one of the answer choices.

Distribute the NOT.

(NOT a) OR (NOT b) OR (NOT c)

This is the other correct answer choice.

The expression evaluates to true when at least one of a, b, and c is false.

(NOT a) OR (NOT b) OR (NOT c)

This is one of the answer choices.

Factor the NOT.

NOT (a AND b AND c)

This is the other correct answer choice.