#### Question

Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.

#### Solution

No of rows = 2^{n}=2^{3} =8

No. of columns = m+ n=3+3= 6

p | q | r | p ∧ q | p ∧ r | (p ∧ q) ∨ (p ∧ r) |

T | T | T | T | T | T |

T | T | F | T | F | T |

T | F | T | F | T | T |

T | F | F | F | F | F |

F | T | T | F | F | F |

F | T | F | F | F | F |

F | F | T | F | F | F |

F | F | F | F | F | F |

In the last column, the truth values of the statement is neither all T nor all F. Hence, it is neither a tautology nor a contradiction i.e. it is a contingency.

Is there an error in this question or solution?

#### APPEARS IN

Solution Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency. Concept: Mathematical Logic - Truth Value of Statement in Logic.