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) !a || !b || !c

(B) !(a || b || c)

(D) !a && !b && !c

(A) !a || !b || !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 && b && c

Add a ! to the entire expression to make it false.

!(a && b && c)

This is one of the answer choices.

Distribute the !.

!a || !b ! !c

This is the other correct answer choice.

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

!a || !b || !c

This is one of the answer choices.

Factor the !.

!(a && b && c)

This is the other correct answer choice.