# rose learns.to('code');

## Day 56 – Truth Tables

Review: Each statement is TRUE (1) or FALSE (0).

• 32 is even. T or 1
• A ⊆ B iff x ∈ B implies x ∈ A F or 0

All connectives take a truth value and output a truth value.It means that depending on the connective, the truth value can change.

## Negation

The negation is always the opposite of the truth value. If p is true (1), then the negation is false (0).

Mathematical Value

\neg P\;=\;1\;-\;P\\P\;=\;1\\therefore,\;\neg P\;=\;1-P\;=0

## Conjunction (and)

In conjunction we will see ∧ (caret), & (and symbol), or . (dot).

Conjunction takes two statements and combine them.

\#\;of\;rows\;=\;2^{number\;of\;statements}

Mathematical Value

p\;\wedge\;q\;=\;min(p,q)

## Disjunction (or)

In disjunction we will see or +.

Takes either or both conditions of p or q.

Mathematical Value

p\;\wedge\;q\;=\;max(p,q)

## Conditional (if, then)

We would normally see or ⊃ symbols.

Mathematical Value

p\;\to\;q\;=\;1\\iff\\p\;\leq\;q

## Biconditional (if and only if, iff)

Symbols used: ↔ ⇔ ≡ ⟺

Mathematical Value

p\;=\;q\;then\;p\;\iff\;q\;=\;1

## Exclusive Or (the idea of or in English)

Symbols used: or

p \neq\;q\;then\;p\;\oplus\;q\;=1

## Latex:

• subset of = ⊆ = \subseteq
• not subset of = ⊈ = \nsubseteq
• element of = ∈ = \in
• not element of = ∉ = \notin
• and = ∧ = \wedge
• or = = \vee
• if and only if = ↔ = \iff
• exclusive or = = \oplus