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Translating Verbal Arguments Into Symbolic Form

Translating Verbal Arguments Into Symbolic Form

Translating Verbal Arguments Into Symbolic Form Video

In geometry, logical arguments can be represented by symbolic notation. In this video, you will learn how to translate logical arguments from verbal form to symbolic form. Click the player button to begin.

View a transcript of this video.

 

Translating If and Only If

The phrase if and only if is represented by the symbol ↔. So how can you use this symbol to translate statements that contain the phrase if and only if into symbolic form? Take a moment to practice the problem below.

Let p represent 3x = 18.
Let q represent x = 6.

Given this information, represent the following statement symbolically:

3x = 18 if and only if x = 6.

When you have your answer, hover your mouse over the rectangle below to reveal the correct answer.

p if and only if q

 

More on Compound Statements

Conjunctions and disjunctions are referred to as compound statements.

Conjunctions

As you learned earlier in this topic, a conjunction is an argument that is formed using the word and. To translate a conjunction into symbolic form, you must use the symbol ∧.

A conjunction a ∧ b is true if both a and b are true. Consider the example below.

Let p represent a square has a total of four sides.
Let q represent a triangle has a total of three sides.

Is p ∧ q true?

When you have your answer, hover your mouse over the rectangle below to reveal the correct answer and explanation.

Yes, p and q is true because both p and q are true.

Disjunctions

Recall that a disjunction is an argument that is formed using the word or. To translate a disjunction into symbolic form, you must use the symbol ∨.

A disjunction a ∨ b is true if either a or b is true. Consider the example below.

Let c represent a rectangle has a total of four sides.
Let d represent a square has a total of three sides.

Is c ∨ d true?

When you have your answer, hover your mouse over the rectangle below to reveal the correct answer and explanation.

A disjunction, a or b is true if either a or b is true. Therefore, c or d is true because c is true.

 

Translating Verbal Arguments Into Symbolic Form Review

Translating Verbal Arguments Into Symbolic Form Review Interactivity

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