Hello,

I am looking to find solution for the below mentioned problems.

Could someone please help me on this?

1.Determine the truth value for each of the following statements. Justify why they are true or provide a counter example to show they are false.
(a) ∀a∈Z:a4 >a3
(b) ∃a,b∈Z:ab=22
(c) ∀a∈Z,∃b∈Z:a−2=b (d) ∀a∈Z,∃b∈Z:ab =10 (e) ∀a∈Z,∃b∈Z:a/b∈Z

2. Consider sets A, B and C, which are pairwise disjoint (i.e. A∩B = A∩C = B∩C = ∅). If X ⊆ A ∪ B and Y ⊆ A ∪ C, show that X ∩ Y ⊆ A.

3. LetsetA={x∈N|x2 <100}andsetB={x∈N|x<20∧xeven}.
(a) Write out both sets in full.
(b) How many elements are in the power sets of A and B? (c) Write out in full the set formed by A ∩ B.
(d) Define in mathematical notation, the set formed by A\B. (e) FindtwosetsXandYsuchthatX∈YandX⊆Y.

4. Determine whether each of these sets is the power set of a set where a and b are distinct. If the answer is positive, state the set for which the given set is a power set:
(a) ∅
(b) {{a}}
(c) {∅,{a}}
(d) {∅,{a},{a}}
(e) {∅,{a},{b},{a,b}}