A sentence that has exactly one truth value: true, which we denote by T, or false, which we denote by F.

Denoted ~P and means 'not P'. Proposition of ~P is true exactly when P is false.

Given propositions P and Q, the [this term] of P and Q is denoted P ^ Q, is the proposition 'P and Q'. It is true exactly when both P and Q are true.

[This term] of P and Q, denoted P v Q is the proposition 'P or Q'. P v Q is true exactly when at least one of P or Q is true.

A propositional form that is true for every assignment of truth values to its components.

A propositional form that is false for every assignment of truth values to its components.

Two propositional forms are [this term] if and only if they have the same truth tables

For propositions P and Q, the [this term] P=>Q is the proposition 'If P, then Q'. It is true iff P is false or Q is true.

In P=>Q, P is this

In P=>Q, Q is this

Let P and Q be propositions. The [this term] of P=>Q is Q=>P

Let P and Q be propositions. The [this term] of P=>Q is (~Q)=>(~P)

For P and Q, the [this term] PQ is the proposition 'P if and only if Q'. P is true exactly when P and Q have the same truth values.

A sentence that contains variables, and will become a proposition only when the variables are assigned specific values

With a universe specified, two open sentences P(x) and Q(x) are [this term] iff they have the same truth set.

Means 'There exists an x such that P(x)' or 'For some x, P(x)'

Means 'For all x, P(x)' and is true iff the truth set of P(x) is the entire universe.

This symbol following the existential quantifier means 'There exists a unique x such that P(x)' and is true iff the truth set of P(x) has exactly one element.

The tautology [P ^ (P=>Q)]=>Q

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