1. This question concerns the basic structures used within 2 specifications. (a) Does the formula [5 marks] VX:N. (X* X > x) of first-order logic evaluate to true? Justify your answer. (b) Let S = {1,2,3,4} and T = {a,b,c} as well as [4 marks] f = {1 H 2,2 6,3 + 0,4 # ay and g= {1 H 6,2 Ha, 3 H C}. Determine for f and g whether or not they are injections from S to T. Justify your an- swers. (c) Give a total surjection from the set {..., -4,-2,0,2,4, ...} of even integers to the set {0, 1, 2, ...} of natural numbers. Justify your answer. [6 marks] (d) Give a sequence o over {a,b,c} such that both [2 marks] ol{a,b} = (a, a, b, b) and ob,c} = (c, b, c,b,c). Justify your answer. (e) Give a bag B such that dom B = {a,b,c,d} and ran B = {1,2,3}. Justify your answer. [3 marks] 1. This question concerns the basic structures used within 2 specifications. (a) Does the formula [5 marks] VX:N. (X* X > x) of first-order logic evaluate to true? Justify your answer. (b) Let S = {1,2,3,4} and T = {a,b,c} as well as [4 marks] f = {1 H 2,2 6,3 + 0,4 # ay and g= {1 H 6,2 Ha, 3 H C}. Determine for f and g whether or not they are injections from S to T. Justify your an- swers. (c) Give a total surjection from the set {..., -4,-2,0,2,4, ...} of even integers to the set {0, 1, 2, ...} of natural numbers. Justify your answer. [6 marks] (d) Give a sequence o over {a,b,c} such that both [2 marks] ol{a,b} = (a, a, b, b) and ob,c} = (c, b, c,b,c). Justify your answer. (e) Give a bag B such that dom B = {a,b,c,d} and ran B = {1,2,3}. Justify your answer. [3 marks]