Wiki's Table of Binary Logical Connectives in Griceian Key

by JLS
for the GC

Again, this below should better be copied and pasted in the right enriched text, but provide way or bear with it. I was trying to see if I could recover some of the nicey displays in wiki.

Table of binary logical connectives

"There are sixteen Boolean functions associating the inputs P and Q with four-digit binary outputs."

1. Contradiction
Notation Equivalent
formulas Truth table Venn diagram
P ¬P Q
0 1
P 0 0 0
1 0 0

2. Tautology
Notation Equivalent
formulas Truth table Venn diagram
P ¬P Q
0 1
P 0 1 1
1 1 1

3. Conjunction
Notation Equivalent
formulas Truth table Venn diagram
P Q
P & Q
P · Q
P AND Q P ¬Q
¬P Q
¬P ¬Q Q
0 1
P 0 0 0
1 0 1

4. Alternative denial Notation Equivalent
formulas Truth table Venn diagram
P ↑ Q
P | Q
P NAND Q P → ¬Q
¬P ← Q
¬P ¬Q Q
0 1
P 0 1 1
1 1 0

5. Material nonimplication
Notation Equivalent
formulas Truth table Venn diagram
P Q
P Q P & ¬Q
¬P ↓ Q
¬P ¬Q Q
0 1
P 0 0 0
1 1 0

6. Material implication
Notation Equivalent
formulas Truth table Venn diagram
P → Q
P Q P ↑ ¬Q
¬P Q
¬P ← ¬Q Q
0 1
P 0 1 1
1 0 1

7. Proposition P
Notation Equivalent
formulas Truth table Venn diagram
P Q
0 1
P 0 0 0
1 1 1

8. Negation of P
Notation Equivalent
formulas Truth table Venn diagram
¬P
~P Q
! 0 1
P 0 1 1
1 0 0

9. Con! verse no nimplication
Notation Equivalent
formulas Truth table Venn diagram
P Q
P Q P ↓ ¬Q
¬P & Q
¬P ¬Q Q
0 1
P 0 0 1
1 0 0

10. Converse implication
Notation Equivalent
formulas Truth table Venn diagram
P Q
P Q P ¬Q
¬P ↑ Q
¬P → ¬Q Q
0 1
P 0 1 0
1 1 1

11. Proposition Q
Notation Equivalent
formulas Truth table Venn diagram
Q Q
0 1
P 0 0 1
1 0 1

12. Negation of Q
Notation Equivalent
formulas Truth table Venn diagram
¬Q
~Q Q
0 1
P 0 1 0
1 1 0

13. Exclusive disjunction
Notation Equivalent
formulas Truth table Venn diagram
P Q
P Q
P Q
P XOR Q P ¬Q
¬P Q
¬P ¬Q Q
0 1!
P 0 0 1
1 1 0

14. Biconditional
Notation Equivalent
formulas Truth table Venn diagram
P Q
P ≡ Q
P XNOR Q
P IFF Q P ¬Q
¬P Q
¬P ¬Q Q
0 1
P 0 1 0
1 0 1

15. Disjunction
Notation Equivalent
formulas Truth table Venn diagram
P Q
P ∨ Q
P OR Q P ¬Q
¬P → Q
¬P ↑ ¬Q Q
0 1
P 0 0 1
1 1 1

16. Joint denial
Notation Equivalent
formulas Truth table Venn diagram
P ↓ Q
P NOR Q P ¬Q
¬P Q
¬P & ¬Q Q
0 1
P 0 1 0
1 0 0

venn diagram formulas