# Table 1 Logical matrices of 16 Boolean operations

Logical connective Logical operator Logical matrix for 2-node
symbol Boolean networks
True $$\left (\begin {array}{cccc} 1&1&1&1 \\ 0&0&0&0 \end {array} \right)$$
False $$\left (\begin {array}{cccc} 0&0&0&0 \\ 1&1&1&1 \end {array} \right)$$
Proposition x 1 x 1 $$\left (\begin {array}{cccc} 1&1&0&0 \\ 0&0&1&1 \end {array} \right)$$
Proposition x 2 x 2 $$\left (\begin {array}{cccc} 1&0&1&0 \\ 0&1&0&1 \end {array} \right)$$
Negation (inhibition) x 1 ¬x 1 $$\left (\begin {array}{cccc} 0&0&1&1 \\ 1&1&0&0 \end {array} \right)$$
Negation (inhibition) x 2 ¬x 2 $$\left (\begin {array}{cccc} 0&1&0&1 \\ 1&0&1&0 \end {array} \right)$$
Conjunction $$\left (\begin {array}{cccc} 1&0&0&0 \\ 0&1&1&1 \end {array} \right)$$
Disjunction (union) $$\left (\begin {array}{cccc} 1&1&1&0 \\ 0&0&0&1 \end {array} \right)$$
Converse implication $$\left (\begin {array}{cccc} 1&1&0&1 \\ 0&0&1&0 \end {array} \right)$$
Material conditional $$\left (\begin {array}{cccc} 1&0&1&1 \\ 0&1&0&0 \end {array} \right)$$
Converse nonimplication $$\nleftarrow$$ $$\left (\begin {array}{cccc} 0&0&1&0 \\ 1&1&0&1 \end {array} \right)$$
Material nonimplication $$\nrightarrow$$ $$\left (\begin {array}{cccc} 0&1&0&0 \\ 1&0&1&1 \end {array} \right)$$
Biconditional $$\left (\begin {array}{cccc} 1&0&0&1 \\ 0&1&1&0 \end {array} \right)$$
Alternative denial $$\left (\begin {array}{cccc} 0&1&1&1 \\ 1&0&0&0 \end {array} \right)$$
Joint denial $$\left (\begin {array}{cccc} 0&0&0&1 \\ 1&1&1&0 \end {array} \right)$$
Exclusive disjunction $$\left (\begin {array}{cccc} 0&1&1&0 \\ 1&0&0&1 \end {array} \right)$$