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i was hoping somebody could help me with these problems

1) Are the following statements true or false?

(a) 2 є S, where

S= {x є R|x is the square root of an integer}

b) ø є {ø}

c) ø c ø

d) {{ø}} c {ø, {ø}}

e) {ø, {ø}, {ø, {ø}}} has the cardinality 4

f) {ø, {a}, {ø,a}} is the powerset of set of cardinaltiy 2

g) if A,B and C are sets such that AuC = BuC and AuC = BnC then A=B

also another problem I had was:

Prove that the square of an odd number is an odd

number using

proof by contradiction

1) Are the following statements true or false?

(a) 2 є S, where

S= {x є R|x is the square root of an integer}

b) ø є {ø}

c) ø c ø

d) {{ø}} c {ø, {ø}}

e) {ø, {ø}, {ø, {ø}}} has the cardinality 4

f) {ø, {a}, {ø,a}} is the powerset of set of cardinaltiy 2

g) if A,B and C are sets such that AuC = BuC and AuC = BnC then A=B

also another problem I had was:

Prove that the square of an odd number is an odd

number using

proof by contradiction

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