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MAT425 Real Analysis L1

Prof. Thistleton

Statements and Connectives

1.

statements

2.

negation (not, $\neg$ )

3.

conjunction (and, $\wedge$ )

4.

disjunction (or, $\vee$ )

5.

implication

6.

logically equivalent, $\equiv$ , if and only if, $\Leftrightarrow$

Proofs

Disjoined Conclusions

Prove the following: $A \Rightarrow (B\ or\ C) \ \ \Leftrightarrow \ \ (A\ and\ not C) \Rightarrow B$

Disjoined Hypotheses (Proof by Cases)

Prove the following: $(A\ or\ B) \Rightarrow C \ \ \Leftrightarrow \ \ (A \Rightarrow C)\ and\ (B \Rightarrow C)$

Prove the following: $x\ \leq\ \mid x \mid$

Open Statements, Universal Quantifier ( $\forall$ ), Existential Quantifier ( $\exists$ )

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William Thistleton
11/10/1998