Hello do you please see the attach the exercise

Thank you

Exercise 1. Write the following formulas; make that the operator of the formula is not the same as the operator of the formula. Eggregation applies only to the predicates in the result formulas. a. 3x (F (x) A -G(x)) b. 32 vxby(-F (x, y) - G(z, x)) Exercise 2. Show that for any integer n and for any number reel n > - 1, it is true that (1 + x) "> 1+n xx. Make a proof by recurrence. Exercise 3 Let A, B, C be three sets. Consider the following propositions p and q: p: if A F B then (An C CBn C) q : si AnB = AnCthen An B = And a. Write the reciprocal of p. b. Show that the reciprocal ofp is false by considering the sets 4 = (2, 4), B = {4, 8), C = (4). c. Show by reasoning through the absurd that the proposition g is true. Exercise 4. (0, 1] represents the interval of real numbers between 0 and 1 Let f f : [0, 1] - 10, 1], 1 1 1 - sirEO, inQ x otherwise Show that f : f = Id [o,1]. Exercise 5. One bag contains 12 discernible shirts: 3 green, 4 red and 5 yellow. In how many different ways can the shirts be removed from the bag buccession? In how many different ways can shirts be removed from the bag knowing that the yellow shirts are removed as a group, i.e., one yellow shirt is removed, all other yellow shirts are removed next, before the remaining shirts of the other two colors are removed? How many ways are there to remove three shirts of different colours