Question

Universal: { 1,2,3,4,5,6,7 } A { 1,3,5,7 } and B { 3,4,5,6 } verify by demorgan law​

Answer 1

Answer:

A=(1,2,3,4)

B=(3,4,5,6)

C=(4,5,6,7,8)

U=(1,2,3,4,5,6,7,8,9,10)

According to DeMorgan's Law

(A∨B)

′

=A

′

∧B

′

A

′

=(∧5,6,7,8,9,10)

B

′

=(1,2,7,8,9,10)

(A∨B)=3,4

(A∨B)

′

=1,2,5,6,7,8,9,10

A

′

∧B

′

=1,2,5,6,7,8,9,10

Hence proved

Answer 2

Answer:

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Step-by-step explanation:

Step-1:Prove using suitable formula of sets.

It is given that,

A∪B = A∪C …(1)

A∩B = A∩C…(2)

Taking  ’∩ C’ on both sides in equation (1)

(A∪B)∩C = (A∪C)∩C

We know that,

(A∪B)∩C = (A∩C)∪(B∩C) and (A∪C)∩C = C

So,

(A∩C)∪(B∩C)=C

(A∩B)∪(B∩C)=C…(3)[From(2))

Again,

Taking  ’∩ B’ on both side in equation (1)

(A∪B)∩B = (A∪C)∩B

B = (A∩B)∪(C∩B)

B = (A∩B)∪(B∩C)

B = C[From (3)]

Hence, proved.