before you comment "part 1 is missing" or "lack of info"

this is the entirety of the question. Also 1 question solve = all the parts from a to c, not just a or a,b or c

Thank You

2. (30 points) Prove/Disprove every one of the following statements. If you believe that a statement is false, provide a counterexample; otherwise provide a full mathematical proof. (a) (10 points) if action a strictly dominates action b for player i, then action b is played with zero probability in any Nash equilibrium. (b) (10 points) If p*,q* are Nash equilibria, then either (p* i, 7x) or (qki,p) is a Nash equilibrium as well. . 1 (c) (10 points) if a, b e A are best responses to P-A(A-i) then so is the mixed strategy given by playing a with probability a and b with probability 1 - a. 2. (30 points) Prove/Disprove every one of the following statements. If you believe that a statement is false, provide a counterexample; otherwise provide a full mathematical proof. (a) (10 points) if action a strictly dominates action b for player i, then action b is played with zero probability in any Nash equilibrium. (b) (10 points) If p*,q* are Nash equilibria, then either (p* i, 7x) or (qki,p) is a Nash equilibrium as well. . 1 (c) (10 points) if a, b e A are best responses to P-A(A-i) then so is the mixed strategy given by playing a with probability a and b with probability 1 - a