Math

These logically equivalent statements can be checked by using a truth table.

$\neg (A\wedge B)\equiv (\neg A)\vee (\neg B)$ $\neg (A\vee B)\equiv (\neg A)\wedge (\neg B)$

Commutative laws

$A\wedge B\equiv B\wedge A$ $A\vee B\equiv B\vee A$

Associative laws

$A\wedge (B\wedge C)\equiv (A\wedge B)\wedge C$ $A\vee (B\vee C)\equiv (A\vee B)\vee C$

Distributive Laws

$A\wedge (B\vee C)\equiv (A\wedge B)\vee (A\vee C)$ $A\vee (B\wedge C)\equiv (A\vee B)\wedge (A\vee C)$

DML for Quantifiers

$\neg (\forall x,P(x))\equiv \exists x,\neg P(x)$ $\neg (\exists x,P(x))\equiv \forall x,\neg P(x)$

ECE124 Digital Circuits

The complement of a sum of variables is equal to the product of the complements of the variables. Stated another way, The complement of two or more ORed variables is equivalent to the AND of the complements of the individual variables, $\overline{XY}=\overline{X}+\overline{Y}$

$\overline{X+Y}=\overline{X}\overline{Y}$