If p is true, then p v p is true. In logical expression
The conjunction is true if at least one is true.
If the p v p is true, then p is true. In logical expression
is equivalent to .
De Morgan's Law says
The conjunction is like you are being offered to have a potato or a potato. There is only one choice, potato.
It's different if the conjuction is , which is like being offered rice or potato. If it's rice then it's not potato. So either way, you get at least one.
is like the same as saying, "If it's a potato, then you get potato or potato."
Here is the De Morgan's Law .
Here is the negation of implication: