Connectives and Truth Values

by Osama M. Khaled — last modified 2022-06-15T09:08:25+01:00

In English, simple statements are combined with connecting words like and to make more interesting compound statements.

Questions #: 20
Pass Score: 80.0%

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 ______

    ∧

    and
    or
    not
    Non of the above

    The below symbol represents ______

    ∨

    and
    or
    not
    Non of the above

    The below symbol represents

    →

    or
    and
    implication
    Non of the above

    What is the name of the following symbol?

    ↔

    equal
    equivalence
    match
    connector

    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

    A
    B
    C
    D

    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

    true, false, true
    false, true, true
    false, false, true
    false, false, false

    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
    True
    False

    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
    True
    False

    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
    a
    b
    c
    d

    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

    F, T, F, T
    F, F, T, T
    T, F, T, T
    T, F, F, T

    Is the following claim correct?

    If A → B is true, then A must be true

    Correct
    Incorrect

    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

    Correct
    Incorrect

    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)
    a
    b
    c
    d

    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

    T, T
    T, F
    F, T
    F, F

    If A = true, then A' = _____

    true
    false
    Invalid connective

    The negation of A is symbolized by

    A'
    A"
    -A
    A-

    The following is a legitimate expression

    A )) ∧ ∧ → BC

    True
    False

    Arrange connectives in order of precedence

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

    What is the main connective in the following formula

    ((A ∨ B) ∧ C) → (B ∨ C')

    1. ∧
    2. ∨
    3. →
    4. '
    5. Parentheses
    a
    b
    c
    d
    e

    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
    a
    b
    c
    d