Question

Determine which of the following statements are true and which are false

a. a⊆a
b. a⊆a,b
c. ∅⊆∅
d. ∅⊆∅
e. ∅⊂∅
f. a⊆℘{a,b)

Answer 1

a. True, b. True, c. False, d. False, e. False, f. False

Step-by-step explanation:

a. True: A set is always a subset of itself. Therefore, a⊆a is true.

b. True: The empty set (∅) is a subset of every set. Therefore, ∅⊆∅ is true.

c. False: The empty set (∅) is not a proper subset of itself. Therefore, ∅⊂∅ is false.

d. False: The empty set (∅) is not a proper subset of itself. Therefore, ∅⊂∅ is false.

e. False: The empty set (∅) is not a proper subset of itself. Therefore, ∅⊂∅ is false.

f. False: The set {a,b} is not a subset of the power set of {a,b}. Therefore, a⊆℘{a,b} is fals