Biconditionals - Logic

Biconditionals

Lessons

Notes:
A biconditional is a conjunction of a conditional and its converse. In symbolic form it would be:

(pq)(p \to q) ˄ (qp)(q \to p)

We can also write it as pqp \leftrightarrow q. In words, we connect pp and qq with "if and only if". A biconditional can be only true if both the conditional and converse is true. Here is a truth table of a biconditional.

pp qq pqp \to q qpq \to p (pq)(p \to q ) ˄ (qp)(q \to p) pq p \leftrightarrow q
T T T T T T
T F F T F F
F T T F F F
F F T T T T
    • a)
      What are Biconditionals
  • 1.
    Forming the Biconditional
    Write a biconditional using the given conditionals:
  • 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

  • 3.
    Truth value of Biconditionals
    Determine the truth value of the following biconditionals:
  • 4.
    Let both pp, qq and rr be statements.
Teacher pug

Biconditionals

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