Discrete Math: Prove the following statements: By Direct Proof: i) For All Natural Numbers p q...

Discrete Math: Prove the following statements:

By Direct Proof:

i) For All Natural Numbers p q & r: if p divides q and q divides r then p divides r.

ii) For All integers a & b: if a = b mod 12, then a = b mod 6;

(show that the converse is not true with an example [if a= b mod 6, then a = b mod12]))

iii)Show that for sets F & G

- If F is a subset of G , then F = F intersection G

- If F = F intersection G, then G = F union G

- If G = F union G, then F is a subset of G

Show that for Real numbers a & b : (a+b)²>=4ab when a &b >=0

Expert Solution

Colby Messinger answered 6 months ago

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