Originally Posted by

**Student122** Hi;

I'm trying to figure out if the following statements are true or not;

**1.** p v 段 = p -> q

**2.** 段 -> 殆 = q -> p

**3.** p v (q -> r) = (p v q) -> (p v r)

Can someone please outline what these lines mean in normal english?

For example, the start of 1 means; p or not q...

I don't know what that little arrow actually means...

Are there any resources online to learn this at __basic__ level?

Thanks in advance,

**appreciate your time!**

Hi Student122,

The little arrow means "implies". $\displaystyle p \rightarrow q$ means p implies q, or simply "if p, then q".

Sometimes it's written $\displaystyle p \implies q$

Do you know what truth table are? Look here: Truth table - Wikipedia, the free encyclopedia

Code:

p | q |not p | not q | p --> q | not p or q | p or not q
---------------------------------------------------------
T | T | F | F | T | T | T
T | F | F | T | F | F | T
F | T | T | F | T | T | F
F | F | T | T | T | T | T

As you can see from the truth table above, your first implication is false.

[1] $\displaystyle p \vee \neg q \equiv p \rightarrow q$ is false.

Their truth values are not the same. Check the truth table.

But this is true: $\displaystyle \neg p \vee q \equiv p \rightarrow q$.

Chech the truth values under their columns.

Try to set up a truth table to verify the other 2.