Test 1 Info

This page contains information pertaining Test 1.

§ 1 Preparing for test 1

§ 2 Sample Test Questions

The section contains samples of some of the problems you will see on the test.

Validity: Determine if the following situations are possible:

A valid argument, whose premises are all tautologies, and whose conclusion is contingent.

A consistent set of sentences that contains two sentences that are not logically equivalent.

Logical Equivalence: Prove the following logical equivalences. Be sure to write out each line and provide justification. Suggestion: $\equiv$ is symmetric. $X \equiv Y$ is the same as $Y \equiv X$. Do whichever way that seems easier.

$A \wedge [B \vee (\neg A \wedge C)] \equiv (A \wedge B)$

$A \equiv [(A\wedge B) \vee (A \wedge \neg B)] \vee \neg [(\neg A \wedge \neg B) \vee (\neg A \wedge B )]$ (credit: Emma)

$(\neg \neg A \vee B) \wedge (C \vee (A \wedge B)] \equiv (A \wedge C) \vee B$ (credit: Jin)

Determine the logical status of the following sentences using truth tables. You are encouraged simplify the sentence using logical laws before making a truth table for it (though for some it would be faster just to do a table). Justify your steps.

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

$(A \leftrightarrow A )\to (B \leftrightarrow \neg B)$