Question

Write TRUE/FALSE. PLEASE JUSTIFY ALSO? (1) every set has a proper subset. (2) if x belongs to A and A belongs to B , then x belongs to A.

Answer 1

(1) false
(2) true, X=A   A=B then X=b

Answer 2

Answer:

FALSE   - every set has a proper subset.

TRUE -  if x belongs to A and A belongs to B , then x belongs to A.

Step-by-step explanation:

1)   every set has a proper subset.

Proper Subset:  Any subset B of any given set A  is called a Proper subset if

B ⊂A but  B ≠ A.

Which implies A at least has one extra element then B, which is not in set B.

Also, Null Set (Ф) is the subset of every set.

But the null set Ф has no subsets.

So, its FALSE that every set has a proper subset.

2) if x belongs to A and A belongs to B , then x belongs to A.

if x ∈ A, it implies x is an element of the set A.

and, given that A ⊂ B

⇒ x is also an element of B.

So, its true that the arbitrary element x also belongs to set B.  

⇒ x ∈ B

So, the statement is TRUE.