OR (inclusive)

A |
B |
A or B |
~A |
~B |

T |
T |
T |
F |
F |

T |
F |
T |
F |
T |

F |
T |
T |
T |
F |

F |
F |
F |
T |
T |

Argument

A or B

~B

Therefore, A

To demonstrate with the truth table, look at columns 3 and 5 (premises) and 1 (conclusion). Look at all cases when there are T in 3 and 5. If there's always a T in 1, then it is a valid arg (which it is).

This is not a valid arg:

A or B

A

Therefore, B

To demonstrate, look at columns 1 and 3 (premises) and 2 (conclusion). Notice in row 2 that you have T, F, T... so both premises can be true when the conclusion is false.

AND: try this yourself.

A |
B |
A and B |
~A |
~B |

T |
T |
? |
F |
F |

T |
F |
? |
F |
T |

F |
T |
? |
T |
F |

F |
F |
? |
T |
T |

Is this argument valid:

A and B

A

Therefore, B

Is this argument valid:

A

B

Therefore, A and B