# What is P and Q in truth table?

## What is P and Q in truth table?

Conditional Propositions – A statement that proposes something is true on the condition that something else is true. For example, “If p then q”* , where p is the hypothesis (antecedent) and q is the conclusion (consequent).

**What does P → Q mean?**

In conditional statements, “If p then q” is denoted symbolically by “p q”; p is called the hypothesis and q is called the conclusion. For instance, consider the two following statements: If Sally passes the exam, then she will get the job. If 144 is divisible by 12, 144 is divisible by 3.

**What does P ∧ Q mean?**

P and Q

P ∧ Q means P and Q. P ∨ Q means P or Q. An argument is valid if the following conditional holds: If all the premises are true, the conclusion must be true.

### When P is true and Q is false then PQ?

In the truth tables above, there is only one case where “if P, then Q” is false: namely, P is true and Q is false….IF…., THEN….

P | Q | If P, then Q |
---|---|---|

F | T | T |

F | F | T |

**What is the inverse of P → Q?**

The inverse of p → q is ¬p → ¬q. If p and q are propositions, the biconditional “p if and only if q,” denoted by p ↔ q, is true if both p and q have the same truth values and is false if p and q have opposite truth values.

**Is P → Q → [( P → Q → Q a tautology?**

(p → q) and (q ∨ ¬p) are logically equivalent. So (p → q) ↔ (q ∨ ¬p) is a tautology.

## What is the truth value of the compound proposition P → Q ↔ P if P is false and Q is true *?

Tautologies and Contradictions

Operation | Notation | Summary of truth values |
---|---|---|

Negation | ¬p | The opposite truth value of p |

Conjunction | p∧q | True only when both p and q are true |

Disjunction | p∨q | False only when both p and q are false |

Conditional | p→q | False only when p is true and q is false |

**When p is false and q is true then p or q is true quizlet?**

If p^q is true, then both p and q must be true, therefore p is true. If p^q is true, then both p and q must be true, therefore q is true. For pVq to be true and q is not true, then at least one of the values must be true which is p.

**Is P then not Q?**

“If p, then not q” is equivalent to “No p are q.” Example: “If something is a poodle, then it is a dog” is a round-about way of saying “All poodles are dogs.”

### What is the truth value of p and q if/p is true and q is false?

So because we don’t have statements on either side of the “and” symbol that are both true, the statment ~p∧q is false. So ~p∧q=F. Now that we know the truth value of everything in the parintheses (~p∧q), we can join this statement with ∨p to give us the final statement (~p∧q)∨p….Truth Tables.

p | q | p∧q |
---|---|---|

F | T | F |

F | F | F |

**When p is false and q is true then p or q is?**