set theory

Question

Answer 1

A) FALSE ---element 0 is not present in an empty set.  
B) FALSE ---empty set is not present as an element {0}
C) FALSE --- {0} is not subset of {}.if it is not subset,it cannot be a proper subset
D) TRUE --- empty set is a subset of every set and since the set contains one more element [ 0 ] , is a proper subset.
E) FALSE --- {0} is not present in the set.Only 0 is present.
F) FALSE --- {0} is a subset of {0},not a proper subset.
G) TRUE

Comments

why b) not correct?

 it is set {0}

not an element 0

Answer 2

a)False --- 0 cannot belong to a set which is empty set

b)False --- when belongs is used the element should be present in the set

c)False --- a set with element cannot be subset of empty set

d)True --- empty set is subset of every set

e)False --- 0 belongs to {0} but not {0}

f)False--- every set is a subset of itself but not proper subset of itself

g) True --- here same as previous but empty set instead of 0