Question

A=(x:x is a prime factor of 7854) B=(x:x is a prime factor of 2090) prove that AuB-AnB=(A-B)u(B-A)

Answer 1

Here,

A = {x:x is a prime factor of 7854}

=> A = {2, 3, 7, 11, 17}

And,

B = {x:x is a prime factor of 2090}

=> B = {2, 5, 11, 19}

Now,

AuB = {2, 3, 5, 7, 11, 17, 19}

AnB = {2, 11}

=> AuB-AnB = {3, 5, 7, 17, 19} --- (1)

And,

A-B = {3, 7, 17}

B-A = {5, 19}

=> (A-B)u(B-A) = {3, 5, 7, 17, 19} --- (2)

From 1 and 2, we get

AuB-AnB = (A-B)u(B-A)

Hence proved

Answer 2

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Step-by-step explanation:

Here,

A = {x:x is a prime factor of 7854}

=> A = {2, 3, 7, 11, 17}

And,

B = {x:x is a prime factor of 2090}

=> B = {2, 5, 11, 19}

Now,

AuB = {2, 3, 5, 7, 11, 17, 19}

AnB = {2, 11}

=> AuB-AnB = {3, 5, 7, 17, 19} --- (1)

And,

A-B = {3, 7, 17}

B-A = {5, 19}

=> (A-B)u(B-A) = {3, 5, 7, 17, 19} --- (2)

From 1 and 2, we get

AuB-AnB = (A-B)u(B-A)

Hence proved