Question

Assume that a, b, and c have been declared and initialized with int values. The expression

!(a > b || b <= c)
is equivalent to which of the following?

a. a > b && b <= c
b. a <= b || b > c
c. a <= b && b > c
d. a < b || b >= c
e. a < b && b >= c

Answer 1

The expression !(a > b || b <= c) is equivalent to a <= b && b > c, as shown by distributing the negation symbol and simplifying each part of the expression.

Step-by-step explanation:

The given expression is !(a > b || b <= c). To determine the equivalent expression, we can distribute the negation symbol to each part of the expression. This gives us (!(a > b)) && (!(b <= c)). Now we can simplify each part:

1. !(a > b) is equivalent to a <= b. This means that if a is not greater than b, then it must be less than or equal to it.

2. !(b <= c) is equivalent to b > c. This means that if b is not less than or equal to c, then it must be greater than it.

Combining the simplified parts, we get a <= b && b > c. Therefore, the given expression is equivalent to c. a <= b && b > c

Answer 2

The expression !(a > b || b <= c) is equivalent to a <= b && b > c by applying De Morgan's Laws, which means the correct answer is option c.

Step-by-step explanation:

The expression !(a > b || b <= c) involves logical operators and represents a logical negation (NOT) of a disjunction (OR). According to De Morgan's Laws, negating a disjunction is equivalent to a conjunction (AND) of the negations. Thus, to find an equivalent expression, we negate each part of the original expression and change the OR to an AND.

The negated expression becomes a <= b for the first part (negating a > b) and b > c for the second part (negating b <= c). When we combine these negated parts with an AND, we get a <= b && b > c, which means the correct answer is option c.