Question

Plzzz help me...... .. its urgent guys....today i have to submit it...

Answer 1

Answer:

Given:

A=(x∈W/x<2} , B={ x∈N/1<x≤4} and C={3,5}

Verify that:

AX(BUC) = (AXB) U (AXC)

Solution:

A=(x∈W/x<2} => A= {0,1}

B={ x∈N/1<x≤4} => B= {2,3,4}

• AX(BUC)= {0,1} X{2,3,4,5} = {(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)}  ---> 1

• (AXB) U (AXC)= {0,1}X{2,3,4} U {0,1}X{3,5}=
• {(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)} U {(0,3), (0,5),(1,3),(1,5)}=
• {(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)} ---> 2

As we see 1 and 2 are equal, hence verified