Question

Consider the statement P(x) defined as 'x ≤ 4.' Assess the truth values for the following:

a) P(0)
b) P(4)
c) P(6)

Analyze each case individually, applying the given statement to determine whether it is true or false. Discuss the reasoning behind each truth value in the context of the defined statement
P(x) and the specific values of x provided.

Answer 1

The statement P(x) 'x ≤ 4' is true for P(0) and P(4) and false for P(6), based on comparing each value with 4 as per the given inequality.

Step-by-step explanation:

The statement P(x) is defined as 'x ≤ 4.' To assess the truth values for the given instances:

1. P(0): Since 0 is less than or equal to 4, P(0) is true.
2. P(4): Since 4 is equal to 4, P(4) is also true.
3. P(6): However, 6 is not less than or equal to 4, so P(6) is false.

The reasoning is based on the comparison of each value of x with the number 4, adhering to the inequality ≤ (less than or equal to).