Question

using venn diagram, verify the distributive law for three given non - empty sets​

Answer 1

SOLUTION

Using venn diagram, verify the distributive law for three given non - empty sets

EVALUATION

Let three given sets are A , B , C

Distributive law on set theory states that

A ∩ ( B U C ) = ( A ∩ B ) U ( A ∩ C )

PROOF

STEP : 1

First we draw vertical lines in the whole areas of B and C so as to represent ( B U C ) ( Refer to the Figure 1 )

STEP : 2

Now we draw horizontal lines in the whole area A .

Thus the double hatched area in Figure 2 represents area common A and ( B U C ) that is A ∩ ( B U C )

STEP : 3

Again we draw horizontal lines in the area common to A and B so as to represent the set ( A ∩ B ) ( Refer to the Figure 3 )

STEP : 4

Now we draw vertical lines in the area common to A and C so as to represent the set ( A ∩ C )Then the whole hatched area in Figure 4 represents ( A ∩ B ) U ( A ∩ C )

STEP : 5

Hence we observe that the double hatched area in Figure 2 is equal to the total hatched area in Figure 4

Hence proved

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If A, B and C are any three sets

then prove the following using venn-diagram

A∩(BUC) = (A∩B) U (A∩C)

https://brainly.in/question/23234089

2. If A and B are two sets then A-B =B-A if

https://brainly.in/question/28848928