This is a old assignment my roomate had from school, I was interested in Logic and started to read his notes and books and came across this assignment. I tried to figure it out but I failed according to him. So if anyone here could help me out it would be appreciated thanks!

Construct a Truth-table that demonstrates whether (1) is truth functionally true, false, or indeterminate. Explain why your truth-table demonstrates the intended conclusion.

~(C&~C)

Construct a Truth-table that demonstrates whether (2) is true or false. The symbol |= stands for truth-functional entailment. Explain why your truth table demonstrates the intended conclusion.

{(B >C),B} |= C

Note: > is Material implication

Consider the following argument. Jones or sally has the highest exam score. Jones scores higher than sally only if he did not play soccer over the weekend. Since he played soccer, Sally has the highest score.

a) Construct an abbreviation scheme, and symbolize the argument in standard form.

b) Construct a truth-table that demonstrates whether the argument is valid or invalid. Explain why your truth-table demonstrates the intended conclusion.

Consider the following set of sentences. {Neither Smith nor Jones is happy, Brown is unhappy provided that Jones is Unhappy, Smith is happy provided that Brown is unhappy}.

a) Construct an abbreviation scheme, and symbolize each sentence in the set.

b) Construct a truth-table that demonstrates whether the set is truth-functionally consistent or inconsistent. Explain why your truth-table demonstrates the intended conclusion.