Question

if U= {1,2,3,4,5,6,7,8},A={2,4,6,8},B={1,3,5,7} prove De morgan's law​

Answer 1

Step-by-step explanation:

Hint: Here to verify de morgan's law we will find the equation that we need to prove and then through step by step calculations whether Left hand side is equal to the right hand side. While solving this problem we will consider that A∪B

means all the elements belongs to either set A and B or both while A∩B

means all the elements common to set A and B. Lastly the problem will be solved by comparing the equation and this verifying Demorgan’s Law.

Formula Used: In order to verify Demorgan’s law in the given sets we can use the form

I. (A∪B)′

= A′∩B′

II. (A∩B)′

= A′∪B′

Complete step by step solution:

Here in the above question as we know there are three given set which are

A = { 1,2,3,4} B = { 3,4,5,6} C = { 4,5,6,7,8}

The universal set given is n = { 1,2,3,4,5,6,7,8,9,10}

So in order for solving the above equation we need to prove

(A∪B)′

= A′∩B′

Here A′

contains of all the elements in the universal set except those which are in set A

A′

= {5,6,7,8,9,10}

Same goes with B'

which contains of all the elements of universal except those which are in set B

B′={1,2,7,8,9,10}

So, on LHS we get (A∪B)′

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

And on RHS we get A′∩B′

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

Similarly,

(A∩B)′

= {3,4}

A′∪B′

= {3,4}

Hence it is verified that L.H.S is equal to R.H.S thus verifying Demorgan’s law.

Note: Remember that each sign holds value of its own and distribute the numbers from the given sets carefully without committing mistakes. While solving the above equation be careful with the signs and their significance so that the calculation or while separating the sets mistake is avoided and be clear with the representation of AB, A' or B'

etc.