Logical and in the context of Distributive property

⭐ Core Definition: Logical and

In logic, mathematics and linguistics, and ( $\wedge$ ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as $\wedge$ or $\&$ or $K$ (prefix) or $\times$ or $\cdot$ in which $\wedge$ is the most modern and widely used.

The and of a set of operands is true if and only if all of its operands are true, i.e., $A\land B$ is true if and only if $A$ is true and $B$ is true.

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Logical and in the context of Distribution (logic)

In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality $x\cdot (y+z)=x\cdot y+x\cdot z$ is always true in elementary algebra.For example, in elementary arithmetic, one has $2\cdot (1+3)=(2\cdot 1)+(2\cdot 3).$ Therefore, one would say that multiplication distributes over addition.

This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields. It is also encountered in Boolean algebra and mathematical logic, where each of the logical and (denoted $\,\land \,$ ) and the logical or (denoted $\,\lor \,$ ) distributes over the other.

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Logical and in the context of Distributive property

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⭐ Core Definition: Logical and

Logical and in the context of Distribution (logic)