How do I solve this logical operator problem?

Question

My professor gave us a logical operator worksheet from my C++ clas and I got stumped on this problem. If x = -2, y = 5, z = 0, and t = -4, what is the value of each of the following logical expressions?

3 * y / 4 < 8 && y >= 4

I get stuck on this step after I plug everything in. 3 < 8 && 5

I know that on the left 3 * 5= 15, and 15 / 4 = 3. Now the other side is where I get stuck at. I know 5 is true since it's greater than or equal to 4. But I don't know what to do with next when its 8 && 5. Can anyone help?

Answer 1

You can put parenthesis around the various sub-expressions in your expression by following the order of precedence of operators and their associativity .

3 * y / 4 < 8 && y >= 4

is

(3 * y) / 4 < 8 && y >= 4

is

((3 * y) / 4) < 8 && y >= 4

is

(((3 * y) / 4) < 8) && y >= 4

is

(((3 * y) / 4) < 8) && (y >= 4)

That should give you a clear guideline of what the expression should evaluate to.

Answer 2

This seems to be an exercise in operator precedence. When precedence is taken into account, the statement 3 * y / 4 < 8 && y >= 4 is equivalent with

(((3 * y) / 4) < 8) && (y >= 4)

Substituting the variables, we have

(((3 * 5) / 4) < 8 && (5 >= 4)

After doing the math, we end up with

(3 < 8) && (5 >= 4)

3 is indeed lesser than 8, and 5 is indeed greater or equal than 4, so both sides of boolean and are true, and the whole expression is evaluated to true.