Question

A = {multiples of 2}, B = {multiples of 3), C = {multiples of 7}.
If n(A n B n C} = 1 what can you say about $(the universal set).

Answer 1

Let's check the sets

• A={2,4,6,8,..}
• B={3,6,9..}
• C={7,14,21..}

Find LCM

• 2×3×7=42

• (AnBnC)={42}

Recreate the sets

• A={2,4,6,8,10,12..,42}
• B={3,6,9,..,42}
• C={7,14..42}

Now

• n(A)=21
• n(B)=14
• n(C)=6

Hence

Universal Set =U

$\\ \sf\longmapsto U\in R^{+}-\{2,3,4,6,7,8,9,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40 ,42\}$