Connectives and Truth Values

In English, simple statements are combined with connecting words like and to make more interesting compound statements.
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The truth value of a compound statement depends on the truth values of its parts and which connecting words are used. If we combine the two true statement, “Dinosaurs are big,” and,
“soccer balls are round,” we would consider the resulting statement, “Dinosaurs are big and soccer balls are round,” to be true.

The below symbol represents ______

∧

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Explanation

The below symbol represents ______

∨

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The below symbol represents

→

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What is the name of the following symbol?

↔

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Select the right conjunction form

A = Samir is tall

B = Tamer is short

Samir is tall and Tamer is short

a) A ∧ B         b) A ∨ B         c) A → B           d) A ¬ B

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Explanation

What is the truth value of the following conjunctions?

  1. If A is true and B is false, what truth value would you assign to A ∧ B?
  2. If A is false and B is true, what truth value would you assign to A ∧ B?
  3. If A and B are both false, what truth value would you assign to A ∧ B?

Choose from the following options

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What is the missing truth value in the following truth table?

A B A ∧ B 
T T T
T F F
F T ?
F F F
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What is the missing truth value in the following truth table?

A B A ∨ B 
T T T
T F T
F T ?
F F F
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Explanation

How do you represent "If statement A, then statement B" in formal logic?

  1. A ¬ B
  2. A ∧ B
  3. A → B
  4. A ∨ B
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Explanation

Consider the following example to fill in the implication truth table

Your friend promised that if he/she passes the exam, then he/she will go to Friday soccer game. If your friend passes the test and goes to watch the soccer game, the remark was true. If your friend passes the test but doesn’t go to watch the soccer game, the remark was false. If your friend doesn’t pass the test, then—whether he/she goes to watch the soccer game or not—you could not claim that the remark was false. You would probably want to give the benefit of the doubt and say that the statement was true. By convention, A → B is considered true if A is false, regardless of the truth value of B.

A B A → B
T T  
T F  
F T  
F F  

 

Choose from the following options which are ordered from top to bottom

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Is the following claim correct?

If A → B is true, then A must be true

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Is the following sentence correct?

Given A → B

while the truth of A implies the truth of B, the truth of B does not imply the truth of A

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Explanation

What does the following expression stand for?

A ↔ B

  1. (A → B) ∧ (B → A)
  2. (A ∧ B) ∨ (B ∧ A)
  3. (A ∨ B) ∧ (B ∨ A)
  4. (A ¬ B) ∨ (B ¬ A)
POINTS (1)

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Explanation

Complete the missing truth values

A B A → B B → A

(A → B) ∧ (B → A)
T T T T T
T F F T ?
F T T F ?
T T T T T

 

which one of the following options which are ordered top down

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If A = true, then A' = _____

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The negation of A is symbolized by

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The following is a legitimate expression

A )) ∧ ∧ → BC

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Explanation

Arrange connectives in order of precedence

  1. ∧ ∨ 
  2. '
  3. →  
  4. connectives within parentheses, innermost parentheses first
  5. ↔ 
drag and drop the selected option to the right place or type it instead
a
b
c
d
e
POINTS (1)

Correct Answer

Explanation

What is the main connective in the following formula

((A ∨ B) ∧ C) → (B ∨ C')

  1. ∧
  2. ∨
  3. →
  4. '
  5. Parentheses
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Explanation

What is the number of rows in a truth table for a well-formed formula that has n different statement letters?

  1. 2 * n
  2. 2 + n
  3. n2
  4. 2n
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Explanation

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