3. At Least One

If M is not selected then, then T must be chosen. You can then take the contrapositive: If T is not selected, then M must do it.

At Least One

Now we’re going to introduce a new concept: combining conditionals. See this example (shown in the next video):

Premise #1

If Matt is NOT in the Office, then Tim is:

~M T

Premise #2

Contrapositive of #1: If Tim is NOT in the Office, then Matt is.

~T M


At least Tim or Matt must be at the office. Note: There’s nothing ruling out T and M being together.

  • Now that you can combine statements, we can do more complex deductions, such as If and Only If.

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