Compound Statements

A compound statement consist of two or more statements linked by logical connectors (and, or, if-then). Here are some examples:

  • 81270 is a multiple of 2 and 5
  • 81270 is a multiple of 3 or 7
  • If 85 is divisible by 7 then 85 is divisible by 17

Now, let’s solve some sums based on the compound statements.

  1. Express the fact that 81270 is a multiple of 3 or 7 is true in Theorem-Proof style.

Theorem: 81270 is a multiple of 3 or 7.

Proof: By division process we see that 81270=27090*3. As 27090 is an integer, we conclude that 81270 is a multiple of 3. Also 81270=11610*7. As 11610 is an integer, we conclude that 81270 is a multiple of 7.

So, the statement 81270 is a multiple of 3 or 7 is true.

2. Express the fact that if 200 000 000 is a multiple of 375 then 400 000 000 is a multiple of 375 is true in Theorem-Proof style.

Theorem: If 200 000 000 is a multiple of 375 then 400 000 000 is a multiple of 375.

Proof: Let us consider a number x, such that 200 000 000=375*x. The following statement implies that 400 000 000=375*2x. So, we conclude that If 200 000 000 is a multiple of 375 then 400 000 000 is a multiple of 375.

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