Question

If P = {3x/x € N;x≤50}, Q = {5x/x € N; x≤30}, then n(P∩Q)​

Answer 1

ABOVE GIVEN PICTURE IS THE SOLUTION FOR THIS QUESTION.

HOPE IT HELPS YOU ..

Answer 2

The answer is n(P∩Q) = 10

Given: P = {3x / x € N;x≤50}  

Q = {5x / x € N; x≤30}

To find: Using above set we need to find n(P∩Q)​

Solution: P = {3x / x € N;x≤50}

Here, to get set P we need substitute x values from 1 to 50 (including 50) in x place as given below

⇒ P = {3(1), 3(2), 3(3), 3(4), 3(5).... 3(50)

Therefore, P = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150 }  

Q = {5x / x € N; x≤30}

⇒ Q = {5(1), 5(2), 5(3), 5(4).....  5(30) }

⇒ Q = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150 }  

⇒ P∩Q = { 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 }  

Therefore, n(P∩Q) = 10

#SPJ2