Question

question 44
which of the following statements are true?
a (x > 0 && x < 10) is same as ((x > 0) && (x < 10))
b (x > 0 || x < 10 && y < 0) is same as ((x > 0 || x < 10) && y < 0)
c (x > 0 || x < 10 && y < 0) is same as (x > 0 || (x < 10 && y < 0))
d (x > 0 || x < 10) is same as ((x > 0) || (x < 10))

Explanation:

In logical expressions, the order of operations follows rules similar to arithmetic. The logical - AND (&&) has higher precedence than logical - OR (||). Parentheses can be used to change the order of evaluation.

• Option A: In both (x > 0 && x < 10) and ((x > 0) && (x < 10)), the expressions are equivalent because the logical - AND operation is applied to the two conditions x > 0 and x < 10 in the same way.
• Option B: In (x > 0 || x < 10 && y < 0), due to the higher precedence of && over ||, it is equivalent to (x > 0 || (x < 10 && y < 0)), not ((x > 0 || x < 10) && y < 0).
• Option C: As mentioned above, (x > 0 || x < 10 && y < 0) is equivalent to (x > 0 || (x < 10 && y < 0)) because of operator precedence.
• Option D: In both (x > 0 || x < 10) and ((x > 0) || (x < 10)), the expressions are equivalent as the logical - OR operation is applied to the two conditions x > 0 and x < 10 in the same way.

Answer:

A. (x > 0 && x < 10) is same as ((x > 0) && (x < 10))
C. (x > 0 || x < 10 && y < 0) is same as (x > 0 || (x < 10 && y < 0))
D. (x > 0 || x < 10) is same as ((x > 0) || (x < 10))