Biconditionals

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Intros
Lessons
  1. Biconditionals Overview:
    What are Biconditionals
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Examples
Lessons
  1. Forming the Biconditional
    Write a biconditional using the given conditionals:
    1. If today is Monday, then yesterday was Sunday.
      If yesterday was Sunday, then today is Monday
    2. If he drives faster than 100 km, then he will get a ticket.
      If he gets a ticket, then he has driven faster than 100 km.
    3. If today is the weekend, then I do not go to school.
      If I do not go to school, then it is the weekend.
  2. You are given 3 statements in symbolic form:

    pp: There is cream in milk
    qq: There is milk in coffee
    rr: There is cream in coffee

    1. Write the conditional (p (p ˄ q)q) \to rr in words.
    2. Write the converse(p (p ˄ q)q) \to rr in words.
    3. Write the biconditional.
  3. Truth value of Biconditionals
    Determine the truth value of the following biconditionals:
    1. x=5x = 5. if and only if x+7=12x + 7 = 12.
    2. If x>5x > 5, if and only if x>2x > 2 .
    3. The triangle is an isosceles, if and only if two sides are equal.
    4. The angle is acute, if and only if the angle is less than 90° degrees.
  4. Let both pp, qq and rr be statements.
    1. If pp is true, qq is true and rr is false, then what is the truth value of the biconditional (p(p ˄ q)q) \leftrightarrowrr ?
    2. If pp is false, qq is true and rr is false, then what is the truth value of the biconditional (p(p ˄ q)q) \leftrightarrowrr ?
    3. If pp is false, qq is false and rr is true, then what is the truth value of the biconditional (p(p ˄ q)q) \leftrightarrowrr ?
    4. If pp is false, qq is false and rr is false, then what is the truth value of the biconditional (p(p ˄ q)q) \leftrightarrowrr ?