I am looking at a question here and I don't entirely know how to answer this ...
We know that:
1) Tautologies are true for all possible values of the logical variables
2) Contradictions are false for all possible values of the logical variables
3) Contingent propositions are neither
Make the following propositions to one of the above.
a ∧ ¬a
a ∧ ¬(b ⇒ a)
a ⇒ b ⇔ ¬a ∨ b
(a ∨ b) ∧ ¬b
a ⇔ ( ¬a ∧ b)
So lets say that:
- a = we are all happy
- b = we bought a new iPad
The first proposition (a ∧ ¬a) would be:
"We are all Happy AND we are all not happy"
These 2 are not true together because ... we can not be happy and not happy at the same time ... so this one is a contradiction
Can someone please explain how I find out the others?