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Question

Answers

(a)

p | q | $p\wedge \left( \sim q \right)$ |

T | T | F |

T | F | F |

F | T | T |

F | F | F |

(b)

p | q | $p\wedge \left( \sim q \right)$ |

T | T | F |

T | F | T |

F | T | F |

F | F | F |

(c)

p | q | $p\wedge \left( \sim q \right)$ |

T | T | F |

T | F | F |

F | T | F |

F | F | T |

(d)

p | q | $p\wedge \left( \sim q \right)$ |

T | T | T |

T | F | F |

F | T | F |

F | F | F |

Answer
Verified

We are asked to find the truth table for $p\wedge \left( \sim q \right)$.

The symbol $''\wedge ''$ means multiplication and $\sim q$ means opposite of the given value of q like if q is true then $\sim q$ is false.

The way of multiplication of p and q is done as follows:

The result of the multiplication of a true statement with a true statement is true.

The result of the multiplication of a false statement with a false statement is false.

The result of the multiplication of a true statement with a false statement is false.

Now, let us symbolize true as â€śTâ€ť and false as â€śFâ€ť and constructing the truth table of $p\wedge \left( \sim q \right)$ we get,

p | q | $p\wedge \left( \sim q \right)$ |

T | T | F |

T | F | T |

F | T | F |

F | F | F |

The explanation of the above table is that:

In the first row, the multiplication of the true statement of p with the false statement of $\sim q$ is false.

You might think that q is given as true then why we have multiplied false because we have to multiply $\sim q$ not q and $\sim q$ is the opposite of q. Like if q is true then $\sim q$ is false.

Similarly, you can explain the truth values of the remaining rows.

p | q | $p\wedge \left( \sim q \right)$ |

T | T | F |

T | F | T |

F | T | F |

F | F | F |

Now, take the second row of this table, if you forgot to consider $\sim q$ then the truth value of q is false, and multiplying false with the true statement of p we get a false statement and which is not the correct value so this is the place where the tendency of making mistakes is pretty high so make sure you wonâ€™t make this mistake.