Question

Let two sets be P={a,e,d,j,k} and Q={k,l,m,e,n} and U={a,c,d,e,j,k,l,m,n} then prove the the De Morgan's law of union using P and Q.

• A.
  $(P\cup Q)\text{'}=c=P\text{'}\cap Q\text{'}$
  
  
• B. $(P\cup Q)\text{'}\ne P\text{'}\cap Q\text{'}$
• C. $(P\cup Q)\text{'}=a=P\text{'}\cap Q\text{'}$
• D. $(P\cup Q)\text{'}=e=P\text{'}\cap Q\text{'}$

Answer 1

The correct option is A

$(P\cup Q)\text{'}=c=P\text{'}\cap Q\text{'}$


De Morgan's law of union states that,

(P∪Q)′=P′∩Q′ where P and Q are two sets.

(P∪Q)′ = ({a,e,d,j,k} ∪ {k,l,m,e,n})′ = ({a,e,d,j,k,l,m,n})′ = {c}

Now,

P′ = {a,e,d,j,k}′ = {c,l,m,n} = {c,l,m,n}

Q′ = {k,l,m,e,n}′ = {a,c,d,j}

P′ ∩ Q′ = {c}