Math Logic and Statements
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Questions and Answers

Which of the following is a statement?

  • $y$ is odd
  • $x^2 = 10$
  • For all real numbers $a$, $a^2 >= 0$ (correct)
  • $x + 10$

    • Which of the following statements has truth value 'T'?

  • $3$ is a prime number (correct)
  • $1$ is an odd number (correct)
  • $1$ is a prime number
  • None of the above

    • For all $x$, $P(x)$ is false if

  • There is a $x$ for which $P(x)$ is true
  • $P(x)$ is false for every $x$ (correct)
  • $P(x)$ is true for only some $x$
  • There is a $x$ for which $P(x)$ is true

    • The symbol '->' represents

    <p>then</p> Signup and view all the answers

    Which of the following is a conditional statement?

    <p>If $2 = 2$ then $2$ is prime</p> Signup and view all the answers

    Which of the following is a conjunction?

    <p>$x$ is odd and $15$ is composite</p> Signup and view all the answers

    Study Notes

    Statements and Truth Values

    • A statement is a sentence that is either true or false, but not both.
    • For example, "For all real numbers $a$, $a^2 >= 0$" is a statement because it is always true.
    • On the other hand, "$x + 10$" is not a statement because it is an expression that can be true or false depending on the value of $x$.

    Truth Values

    • The truth value of a statement is either 'T' (true) or 'F' (false).
    • For example, the statement "$3$ is a prime number" has a truth value of 'T' because it is true.
    • The statement "$1$ is a prime number" has a truth value of 'F' because it is false.

    Conditional Statements

    • A conditional statement is a statement that can be written in the form "if $p$ then $q$".
    • For example, "If $2 = 2$ then $2$ is prime" is a conditional statement.
    • The symbol '->' is often used to represent "if and then" in conditional statements.

    Conjunctions

    • A conjunction is a statement that combines two or more statements using the word "and".
    • For example, "$x$ is odd and $15$ is composite" is a conjunction.
    • The truth value of a conjunction is 'T' only if all the individual statements are true.

    Disjunctions

    • A disjunction is a statement that combines two or more statements using the word "or".
    • For example, "$3 = 0$ or $2$ is even" is a disjunction.
    • The truth value of a disjunction is 'T' if at least one of the individual statements is true.

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    Description

    Test your understanding of mathematical statements and logic with these objective questions. Identify true or false statements, and determine the conditions under which a statement is false.

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