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# Implication and Equivalence watch

1. I've started a cousera course called Introduction to Mathematical Thinking,
I haven't been able to find a active study group so I hoped you could help.

These are some exercises I'm currently working through.

Q1 - . Build a truth table to prove the claim I made earlier that φ ⇔ ψ is true if φ and ψ are both true or both false, and φ ⇔ ψ is false if exactly one of φ, ψ is true and the other false. (To constitute a proof, your table should have columns that show how the entries for φ ⇔ ψ are derived, one operator at a time.)

[Q1](https://i.imgur.com/WLi5xE8.jpg)

Questions: If we can assume that F(alse) = 0, while T(rue) = 1 and equivalence is multiplying the two together then we'll get:
T F => F
T T => T
F T => F
F F => T
but that means that 0 x 0 should equal 1, which it obviously doesn't yet I've heard consistently that F F => T -- can someone clarify where I'm going wrong or where I have misunderstood?

Q2 -Build a truth table to show that (φ ⇒ ψ) ⇔ (¬φ ∨ ψ) is true for all truth values of φ and ψ. A statement whose truth values are all T is called a logical validity, or sometimes a tautology.

[Q2](https://i.imgur.com/tnmvIPC.jpg)

I'm not sure what went wrong?!
Questions: Is there an easy way to ensure that I've included all the correct notations in the truth table?
Q3 - Build a truth table to show that (φ 6⇒ ψ) ⇔ (φ ∧ ¬ψ) is a tautology.

[Q3](https://i.imgur.com/oJf7wkL.jpg)

Again I'm not sure where I'm going wrong here!
Jumping to 9) to stay on the same theme

[Q4](https://i.imgur.com/QrwWU0k.jpg)

I must be misunderstanding something here to keep getting these so wrong, any assistance would be much appreciated.
2. (Original post by JL-W)
I must be misunderstanding something here to keep getting these so wrong, any assistance would be much appreciated.

The format for the url bbcode is here. Look for URL hyperlinking.

Even when I par down what you've put, to get to the url, it doesn't seem to give a valid page on i.imgur.com.
3. I think I may have deleted them in tidying up my imgur account : ( sorry.

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