Class 11

Math

JEE Main Questions

Sets

Show that the following four conditions are equivalent:(i)$A⊂B$ (ii) $AB=φ$ (iii) $A∪B=B$ (iv) $A∩B=A$

**Solution: **Solution: 1 and 2)

A-B$=ϕ$

x$∈$A,x$∈/$B

not possible

A$⊂$B

x$∈$B

A-B=$ϕ$

1 and 3)

$x∈AUB$

$x∈Aorx∈B$

AUB=B

1 and 4)

$x∈A∩B$

$x∈Aandx∈B$

$A=A∩B$

$A⊂B$.