Truth Tables for the Conditional and Biconditional

• The truth table for the conditional: (p → q)

  p	q	p → q
  T	T	T
  T	F	F
  F	T	T
  F	F	T

• The book uses the statement, If you get an A, I will buy you a car.
  • T → T, If you get an A and I will buy you a car is true.
  • F → T, If you don't get an A and I buy you a car is true.
  • F → F, If you don't get an A and I don't buy you a car is true.
  • T → F, If you get an A but I don't buy you a car is false.
• In other words, the statement is true unless I break my promise.
• Construct a truth table for ~q → ~p
• The truth table for the biconditional (p ↔ q)

  p	q	p ↔ q
  T	T	T
  T	F	F
  F	T	F
  F	F	T

• Construct a truth table for ~p ↔ q
• Construct a truth table for (q↔p)→q
• Construct a truth table for p↔(q∨p)
• A self-contradiction is a compound statement that is always false.
• Construct a truth table for (p↔q)∧(p↔~q), is this a self-contradiction.
• A tautology is a compound statement that is always true.
• Construct a truth table for (p∨q)∨(~p∧~q)
• An implication is a conditional statement that is a tautology.
• Construct a truth table for [(p∧q)∧p]→q
• You will arrive at the office on time if and only if you take back roads, or you won't be able to attend the meeting.
  • Give the statement in symbolic form.
  • (p↔q)∨r
  • Build the truth table.
• Determine if ~p → p is a self-contradiction, tautology, implication or none.

Equivalent Statements

• Two statements are equivalentA ⇔B if both have exactly the same truth table values in the answer columns of the truth tables.
• are p∨q and ~(~p∧~q) equivalent?
• are ~p∧~q and ~(p∧q) equivalent?
• DeMorgan's laws state
  • ~(p∧q) ⇔ ~p∨~q
  • ~(p∨q) ⇔ !p∧~q
• Negate the statement: "It is not true that streets are dangerous or there is an ice storm."
• Negate the statement: "The bus does not have an engine or the people do not have money"