Question

Can you please sovle this!!

Answer 1

Step-by-step explanation:

U={1,2,3,4,5,6,7,8,9,10}

A={1,2,3,4}

B={2,4,6,8}

a)(A intersection B)' =A'UB'

A intersection B={2,4}

(A intersection B)'={1,3,5,6,7,8,9,10}

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

B'={1,3,5,7,9,10}

A'UB'={1,3,5,6,7,8,9,10}

hence (A intersection B)'=A'UB'

b)A-B=A-(A intersection B)

A-B={1,3}

A intersection B={2,4}

A-(A intersection B)={1,3}

hence A-B=A-(A intersection B)

c)de Morgan's law:

(AUB)'=A' intersection B'

(AUB)={1,2,3,4,6,8}

(AUB)'={5,7,9,10}

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

B'={1,3,5,7,9,10}

A' intersection B'={5,7,9,10}

hence (AUB)'=A' intersection B'