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 | q | p ⊕ q |

1 | 1 | 0 |

1 | 0 | 1 |

0 | 1 | 1 |

0 | 0 | 0 |

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`