Question

Given the Boolean variables, and these initial values where x=TRUE, y=TRUE, z=FALSE. Indicate whether each expression is TRUE or FALSE.

a. ________ !(y ∥ z)∥ x
b. ________ z && x && y
c. ________ ! y∥ (z∥ !x)
d. ________ z ∥ (x && (y∥z))
e. ________ z ∥ (x ∥(y && z))

Answer 1

a. FALSE b. FALSE c. FALSE d. TRUE e. TRUE

Step-by-step explanation:

a. The expression is FALSE. The truth table for the given expression is:

xyz!(y ∥ z)∥ xTRUETRUEFALSEFALSE

b. The expression is FALSE. The truth table for the given expression is:

xyzz && x && yTRUETRUEFALSEFALSE

c. The expression is FALSE. The truth table for the given expression is:

xyz! y∥ (z∥ !x)TRUETRUEFALSETRUE

d. The expression is TRUE. The truth table for the given expression is:

xyzz ∥ (x && (y∥z))TRUETRUEFALSETRUE

e. The expression is TRUE. The truth table for the given expression is:

xyzz ∥ (x ∥(y && z))TRUETRUEFALSETRUE