Question

et A fa. b. c, d). B = {b.c.d.e) , then n{(A xB)n(BxA)} =​

Answer 1

Answer:

n[(A∩B)×(B∩A)]=9 elements

Step-by-step explanation:

Let A={a,,c,d,e}

and B={1,2,3,4}

and B={1,2,3,4}A×B=(a,1),(a,2),(a,3),(a,4),(b,1),(b,2),(b,3),(b,4),(c,1),(c,2),(c,3),(c,4),(d,1),(d,2),(d,3),(d,4),(e,1),(e,2),(e,3),(e,4)

and B={1,2,3,4}A×B=(a,1),(a,2),(a,3),(a,4),(b,1),(b,2),(b,3),(b,4),(c,1),(c,2),(c,3),(c,4),(d,1),(d,2),(d,3),(d,4),(e,1),(e,2),(e,3),(e,4)∴n(A×B)=n(A)n(B)=20

and B={1,2,3,4}A×B=(a,1),(a,2),(a,3),(a,4),(b,1),(b,2),(b,3),(b,4),(c,1),(c,2),(c,3),(c,4),(d,1),(d,2),(d,3),(d,4),(e,1),(e,2),(e,3),(e,4)∴n(A×B)=n(A)n(B)=20We know that (A×B)∩(B×A)=(A∩B)×(B∩A)

and B={1,2,3,4}A×B=(a,1),(a,2),(a,3),(a,4),(b,1),(b,2),(b,3),(b,4),(c,1),(c,2),(c,3),(c,4),(d,1),(d,2),(d,3),(d,4),(e,1),(e,2),(e,3),(e,4)∴n(A×B)=n(A)n(B)=20We know that (A×B)∩(B×A)=(A∩B)×(B∩A)So,(A×B)∩(B×A)=(A∩B)×(B∩A)

and B={1,2,3,4}A×B=(a,1),(a,2),(a,3),(a,4),(b,1),(b,2),(b,3),(b,4),(c,1),(c,2),(c,3),(c,4),(d,1),(d,2),(d,3),(d,4),(e,1),(e,2),(e,3),(e,4)∴n(A×B)=n(A)n(B)=20We know that (A×B)∩(B×A)=(A∩B)×(B∩A)So,(A×B)∩(B×A)=(A∩B)×(B∩A)Given:Common elements of A and B=3

and B={1,2,3,4}A×B=(a,1),(a,2),(a,3),(a,4),(b,1),(b,2),(b,3),(b,4),(c,1),(c,2),(c,3),(c,4),(d,1),(d,2),(d,3),(d,4),(e,1),(e,2),(e,3),(e,4)∴n(A×B)=n(A)n(B)=20We know that (A×B)∩(B×A)=(A∩B)×(B∩A)So,(A×B)∩(B×A)=(A∩B)×(B∩A)Given:Common elements of A and B=3∴n(A∩B)=3

and B={1,2,3,4}A×B=(a,1),(a,2),(a,3),(a,4),(b,1),(b,2),(b,3),(b,4),(c,1),(c,2),(c,3),(c,4),(d,1),(d,2),(d,3),(d,4),(e,1),(e,2),(e,3),(e,4)∴n(A×B)=n(A)n(B)=20We know that (A×B)∩(B×A)=(A∩B)×(B∩A)So,(A×B)∩(B×A)=(A∩B)×(B∩A)Given:Common elements of A and B=3∴n(A∩B)=3So,n[(A∩B)×(B∩A)]=n(A∩B)n(B∩A)=3×3=9 elements