Using venn diagram verify : An(BuC) =(AnB) u (AnC)
Answers
TO PROVE
Using Venn Diagram
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 and B are two non empty sets then A∪B=B∩A iff
https://brainly.in/question/24020831
2. If A is a set of vowels and B is a set of first five natural numbers then
A and B are comparable sets
A and B are equal set
https://brainly.in/question/28851425