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1. Prove p∧q=q∧p 2. Prove[((∀x)P(x))∧((∀x)Q(x))]→[(∀x)(P(x)∧Q(x))]. Remember to be strict in your treatment of quantifiers .3. Prove...

1. Prove p∧q=q∧p

2. Prove[((∀x)P(x))∧((∀x)Q(x))]→[(∀x)(P(x)∧Q(x))]. Remember to be strict in your treatment of quantifiers

.3. Prove R∪(S∩T) = (R∪S)∩(R∪T).

4.Consider the relation R={(x,y)∈R×R||x−y|≤1} on Z. Show that this relation is reflexive and symmetric but not transitive.

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