If p = (y : 2y \(\geq\) 6) and Q = (y : y -3 \(\geq\) 4), where y is an integer, find p\(\cap\)Q

A.

{3, 4}

B.

{3, 7}

C.

{3, 4, 5, 6, 7}

D.

{4, 5, 6}

Correct answer is C

p = (y : 2y \(\geq\) 6)

2y \(\leq\) 6

y \(\leq \frac{6}{2}\)

y = \(\leq\) 3

and Q = (y : y -3 \(\geq\) 4)

y - 3 \(\geq\) 4

y \(\geq\) 4 + 3

y \(\geq\) 7

therefore p = {3, 4, 5, 6, 7} and Q = {7, 6, 5, 4, 3....}

P\(\cap\)Q = {3, 4, 5, 6, 7}