1. Determine whether the following claims are true or false. If the claim is true, prove it by giving a semi-formal Natural Deduction proof. If the claim is false, prove this by giving a truth assignment. You should not need to create a full truth table for any of these problems. Remember that when writing Natural Deduction proofs, you may only use the eight Natural Deduction inference rules. Hint: Only two of these claims are false. (a) A7-B,--BF -(A + B) (b) (WAX) +-Y,X F-(WAY) (C) F (M+7N) +-(MAN) (d) Z A, -AE-Z (e) 2+ A, B + A, -AE-21-B () PV (Q177 --R), P+RER (g) (FAG) V ( HI), HEGVI (h) XYF(X V Z) Y (i) J+KF (JV-K) K (j) (Bonus) (AAC) D, A1-BE -(A + B)^(C+D) Hint: This one is only moderately difficult and can be solved using constructive techniques (unlike the bonus problem at the end of the assignment). I probably should have made this a non-bonus problem, but I didn't, so you're welcome