Exam 9: Propositional Logic-Propositions

Use the following key to formulate an English statement that corresponds to the given symbolic statement.G: I go out the door.P: I will put the mail in the mailbox.T: I will turn on the water. G $\supset$ (P • T)

Prove the following claim: A conditional with a self-contradictory antecedent must itself be a tautology.

If both conjuncts of a conjunction are contingencies, then the conjunction itself is a:

If both disjuncts of a disjunction are tautologies, then the disjunction itself is a:

The connective used for biconditionals is:

Choose which symbol to use for "provided," "given that," "supposing that," "unless," and "only if."

Prove the following claim: If at least one member of a set of statements is self-contradictory, then the set of statements is inconsistent.

Put the following statement into symbolic notation, using appropriate letters to abbreviate atomic components. The hijackers were not from Cuba.

Choose which symbol to use for "it is not the case that," "it is false that," and "n't."

For the statement below, classify the statement by identifying the main connective and construct a truth table. ~A $\supset$ B

Identify the components and the connective in the following statement.Then put the statement into symbolic form, using appropriate letters to stand for the components. Dan went swimming even though the water was freezing.

If the antecedent of a conditional is a contingency, then the conditional itself is a:

The conjunction of two equivalent statements is itself a:

In the truth table for the statement form p $\equiv$ q, the column of truth values underneath the main connective should be:

For the following statement, identify (a) the atomic statements; (b) the main components; (c) the connectives; and (d) the main connective. A $\equiv$ ~B

Put the following statement in symbolic form using the letters indicated in parentheses: If 7 is less than 10, then 3 is less than 2.(S, T)

For the following statement, identify (a) the atomic statements; (b) the main components; (c) the connectives; and (d) the main connective. (T $\supset$ N) • (P $\bigvee$ C)

If both disjuncts of a disjunction are self-contradictions, then the disjunction itself is a:

A conditional statement where both the antecedent and consequent are equivalent statements is itself a:

If at least one conjunct of a conjunction is a self-contradiction, then the conjunction itself is a: