If p = (y : 2y ≥ 6) and Q = (y : y -3 ≤ 4), where y is an integer, find pQ

Correct Answer is : {3, 4, 5, 6, 7}

Correct Answer is : {3, 4, 5, 6, 7}

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WAEC Mathematics 2013 Paper

Question : 21

Total: 48

If p = (y : 2y

\geq

\leq

\cap

Solution:

Concept:

Solve each inequality for

y

, then find the common integer values.

Explanation:

For

p

2y \geq 6

Divide both sides by 2:

y \geq 3

p = \{3, 4, 5, 6, 7, \dots\}

For

Q

y - 3 \leq 4

Add 3 to both sides:

y \leq 7

Q = \{\dots, 4, 5, 6, 7\}

The intersection

p \cap Q

contains integers that satisfy both

y \geq 3

and

y \leq 7

Thus,

p \cap Q = \{3, 4, 5, 6, 7\}

Answer:

p \cap Q = \{3, 4, 5, 6, 7\}

Option C.

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