Question

U={1,2,3,7,8,9,10,11,12} P={1,3,7} then (1) show the sets U, P and P' by Venn diagram (2) verify (P')'

Answer 1

GIVEN :

U={1,2,3,7,8,9,10,11,12} P={1,3,7} then (1) show the sets U, P and $P^{\prime}$ by Venn diagram (2) verify $(P^{\prime})^{\prime}$

TO FIND :

(1) Show the sets U, P and $P^{\prime}$ by Venn diagram

(2) Verify $(P^{\prime})^{\prime}=P$

SOLUTION :

Given that the sets are U={1,2,3,7,8,9,10,11,12} and P={1,3,7}

1) Show the sets U, P and $P^{\prime}$ by Venn diagram

We know that $P^{\prime}=U-P$

$={\{1,2,3,7,8,9,10,11,12}\}-{\{1,3,7}\}$

The set $P^{\prime}={\{2,8,9,10,11,12}\}$ and it is shown in figure.

2) Verify $(P^{\prime})^{\prime}=P$

Taking LHS $(P^{\prime})^{\prime}$

$P^{\prime}={\{2,8,9,10,11,12}\}$

$(P^{\prime})^{\prime}=U-P^{\prime}$

$={\{1,2,3,7,8,9,10,11,12}\}-{\{2,8,9,10,11,12}\}$

$={\{1,3,7}\}$

= P = RHS

⇒ LHS = RHS

⇒ $(P^{\prime})^{\prime}=P$

$(P^{\prime})^{\prime}=P$ is verified.

Answer 2

Answer:

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