January 2005 - Question 3



If you're unsure what these arrows mean, then lets look at it this way...

I always remember it by calling the arrow "then". For example:
If the arrow looked like this: → then we would say "If P then Q".
If the arrow was pointing the opposite way like this: ← then we would say "If Q then P"
If the arrow was pointing both ways like this: ↔ then we would say "If P then Q and if Q then P"

Let's look at (i) as an example... which of these sounds right to you?

P → Q : If n is an even number then n is a multiple of 4.
P ← Q : If n is a multiple of 4 then n is an even number.
P ↔ Q : If n is an even number then n is a multiple of 4 and if n is a multiple of 4 then n is an even number.

If you're unsure then test it out...

P → Q : an even number is 2. 2 isn't a multiple of 4 so it can't be this...
P ← Q : ...it's got to be this!

Now try (ii) on your own and scroll down for the answer...

P → Q : If B is a right-angle then AB2 + BC2 = AC2.
P ← Q : If AB2 + BC2 = AC2 then B is a right-angle.
P ↔ Q : If B is a right-angle then AB2 + BC2 = AC2 and if AB2 + BC2 = AC2 then B is a right-angle.









It would be P ↔ Q!

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