Question

If the universal set={1 2 3 4 5 6 7} A={1 2 5 7} B={3 4 5 6} verify (A union B)'=A' intersection B'

Answer 1

this is your solution for the following information

Answer 2

Verified - $(A\cup B)'=A'\cap B'=\phi$

Step-by-step explanation:

Given : If the universal set={1 2 3 4 5 6 7} A={1 2 5 7} B={3 4 5 6}.

To verify : (A union B)'=A' intersection B'

Solution :

The universal set U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

A' are the elements which is not in A,

A' ={3,4,6}

B' are the elements which is not in B,

B'={1,2,7}

Now taking LHS,

$LHS=(A\cup B)'$

Union means the set of all elements in the collection.

$(A\cup B)=\{1,2,3,4,5,6,7\}=U$

Now, (A union B) not are the elements which is not in A union B or U.

i.e. $LHS=(A\cup B)'=\phi$

Now taking RHS,

$RHS=A'\cap B'$

A' ={3,4,6} and B'={1,2,7}

Intersection is the common elements in both the sets.

$RHS=A'\cap B'=\phi$

So, LHS=RHS

Hence verified.

#Learn more

Let U={1,2,3,4,5,6,7},A={1,3,5,7} and B={0,2,3,5,7},find the following sets. 1.A' 2.B' 3.A'intersectionB' 4.A'unionB' 5. (A union B)' 6.(A intersection B)' 7.(A')' 8.(B')'

https://brainly.in/question/4326205