Distributivity of Conjunction

logic propositional-calculus

Solution 1:

There are two distribution laws:

  • Conjunction distributes over disjunction: $x\land (y\lor z)=(x\land y)\lor(x\land z)$

  • Disjunction distributes over conjunction: $x\lor (y\land z)=(x\lor y)\land(x\lor z)$

Also recall that conjunction and disjunction are both commutative.

  • $x\land (y\lor z)=(y\lor z)\land x=(y\land x)\lor(z\land x)=(x\land y)\lor(x\land z)$

  • $x\lor (y\land z)=(y\land z)\lor x =$ et cetera

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