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
