Answer:
1.U={1,2,3,4,5}
A={2}
B={2,3}
C={4,5}
2.U={1,2,3,4}
A={1,2}
B={2,3}
C={4}
Step-by-step explanation:
We are given that [tex]A\cap (B\cup C)[/tex] and [tex]A\cup (B\cap C)[/tex]
are different sets
1.We have to construct a universe set U and non empty sets A,B and C so that above set in fact the same
Suppose U={1,2,3,4,5}
A={2}
B={2,3}
C={4,5}
[tex]B\cap C=\phi[/tex]
[tex]B\cup C=[/tex]{2,3,4,5}
[tex]A\cap (B\cup C)[/tex]={2}[tex]\cap[/tex]{2,3,4,5}={2}
[tex]A\cup (B\cap C)[/tex]={2}[tex]\cup\phi [/tex]={2}
Hence, [tex]A\cap (B\cup C)=A\cup (B\cap C)[/tex]
2.We have to construct a universe set U and non empty sets A,B and C so that above sets are in fact different
Suppose U={1,2,3,4}
A={1,2}
B={2,3}
C={4}
[tex] B\cap C=\phi[/tex]
[tex]B\cup C[/tex]={2,3,4}
[tex]A\cup (B\cap C)[/tex]={1,2}[tex]\cup \phi [/tex]={1,2}
[tex]A\cap (B\cup C)[/tex]={1,2}[tex]\cap[/tex] {2,3,4}={2}
Hence, [tex]A\cap (B\cup C)\neq A\cup (B\cap C)[/tex]
