Question

Please answer the question with full method.Please don't give spam/meaningless answers.​

Answer 1

Step-by-step explanation:

Given:

U ={x | x€ N,1<x<10}

A={x|x=n², n€N,1<n<4}

B={x|x is an even number,x<10}

To find: Verify De Morgan's laws.

Solution:

Step 1: Write given sets in roaster form.

U ={2,3,4,5,6,7,8,9}

A={4,9}

B={2,4,6,8}

Step 2: Write De-Morgan's law

$\boxed{\bold{\red{(A \cup B)'=A'\cap B'}}}$

Find LHS first,

$(A \cup B)$={2,4,6,8,9}

$(A \cup B)'$={3,5,7}...eq1

From RHS

A'={2,3,5,6,7,8}

B'={3,5,7,9}

$A'\cap B'$={3,5,7}...eq2

Since,

eq1=eq2

Hence, it has been verified that

$(A \cup B)'=A'\cap B'$

Step 3: Write second De-Morgan's law

$\boxed{\bold{\red{(A \cap B)'=A'\cup B'}}}$

Find LHS first,

$(A \cap B)$={4}

$(A \cap B)'$={2,3,5,6,7,8,9}...eq3

From RHS

A'={2,3,5,6,7,8}

B'={3,5,7,9}

$A'\cup B'$={2,3,5,6,7,8,9}...eq4

Since,

eq3=eq4

Hence, it has been verified that

$(A \cap B)'=A'\cup B'$

Final answer:

Verification of De-Morgan's laws has been done.

Hope it helps you.

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