Question

Which of the following Boolean expressions are equivalent to the expression num ≥ 15 ?Select two answers.(A) (num > 15) AND (num = 15)(B) (num > 15) OR (num = 15)(C) NOT (num < 15)(D) NOT (num < 16)

Answer 1

To determine the equivalent Boolean expressions to 'num ≥ 15,' we need to evaluate each option. The correct equivalent expressions are (B) (num > 15) OR (num = 15) and (C) NOT (num < 15).

Step-by-step explanation:

To determine which Boolean expressions are equivalent to the expression num ≥ 15, we need to evaluate each option.

1. (A) (num > 15) AND (num = 15) will be true only if both conditions are satisfied, but num cannot be greater than 15 and equal to 15 at the same time, so this expression is not equivalent.
2. (B) (num > 15) OR (num = 15) will be true if either condition is satisfied. In this expression, if num is greater than or equal to 15, then the expression is true, so this is one of the correct equivalent expressions.
3. (C) NOT (num < 15) will be true if num is not less than 15. This expression is equivalent to num ≥ 15.
4. (D) NOT (num < 16) will be true if num is not less than 16. This expression is not equivalent to num ≥ 15 because it allows for values greater than 15.

Therefore, the equivalent Boolean expressions to num ≥ 15 are (B) (num > 15) OR (num = 15) and (C) NOT (num < 15).

Answer 2

The correct answers are (B) and (C).

(num > 15) OR (num = 15)

NOT (num < 15)

1. (B) (num > 15) OR (num = 15)

This expression is true if either "num is greater than 15" or "num is equal to 15", satisfying the condition of "num ≥ 15".

2. (C) NOT (num < 15)

This expression uses De Morgan's Law, which states that the negation of an inequality can be expressed as the opposite inequality with swapped signs. Therefore, "NOT (num < 15)" is equivalent to "num ≥ 15".