QUIZ 1.1 Logical Form and Logical Equivalence

Suppose $$x$$ is a particular real number. Let $$p=(0\lt x),$$ $$q=(x\lt 10),$$ $$r=(x=10)$$. Choose the correct statement below that represents $$(0\lt x\leq10)$$.

$$p\wedge q$$

$$(q\vee r)\wedge p$$

$$p\wedge (q \wedge r)$$

$$p\vee (q \vee r)$$

An or statement is

True only when both components are true

True only when exactly one component is true

False only when both components are false

False only when exactly one component is false

In propositional logic, which of the following is considered a statement?

4 + 3 = 1

a - b > 2

She is an EZLOGIC developer.

Is this a statement?

Given $$p=0$$ and $$q=1$$, evaluate:
1. $$\sim p$$ ___
2. $$\sim p \vee q$$ ___
3. $$\sim(\sim p \vee q)$$ ___
4. $$q \vee (\sim(\sim p \vee q))$$ ___

1 0 0 1

1 0 1 0

1 1 0 1

1 1 0 0

Given statements $$p$$ and $$q$$, the logical equivalence $$p \wedge p \equiv p$$ holds and is known as the:

Identity Law

Idempotent Law

Universal-bound Law

Conjunction Law

Which of the following negates $$3\lt x\leq7$$ ?

-3 ≥ x > 7

-3 > x or x ≥ 7

-3 ≥ x or x > 7

-3 ≥ x and x > 7

The Exclusive OR of $$p$$ and $$q$$, denoted by $$p\oplus q$$, is the proposition that is True when _____ and is False otherwise.

exactly one of p and q is true

at least one of p and q is true

at least one of p and q is false

both of p and q are false

Construct a truth table for $$(p \wedge q) \vee \sim r$$. Question: How many "T"s are there in the last column "$$(p \wedge q) \vee \sim r$$"?

3 or below

6 or above

A _____ is a declarative sentence (a sentence that declares a fact or states an argument) that is either true or false, but not both.

A _____ is a statement form that is always true regardless of the truth values of the individual statements substituted for its statement variables.

QUIZ 1.1:
Logical Form and Logical Equivalence

QUIZ 1.1:
Logical Form and Logical Equivalence

QUIZ 1.1 Logical Form and Logical Equivalence