please help me with these 1. Predicates and Quantifiers (7 points) (1) (3 points

Question

please help me with these

1. Predicates and Quantifiers (7 points) (1) (3 points) Let L( denote the statement "x has used LaTeX." and D denote the domain of a students in our class. Express each of these quantified propositions in English: (a) VrED : L(x) (b) 3ED: L(x) (2) (2 points) Let Q(x) denote the statement "2 > 3r" and Z denote all integers (i.e., -3,-2,-1,0,1,2,3,..). Determine the truth value of each of these statements (a) Q(2) (b) Q(4) (3) (2 points) Translate the following statements to English where B(r) is "r understands boolean algebra" and M(x) is "r has taken discrete math" and the domain D is all students at UTSA (a) VIED : (M(z) B(z))

Explanation / Answer

1. a) All the students have used LaTex
   b) No student has used LaTex
   c) There are some students who have not used LaTex

2. a) Q(2) - false   (2^2 = 4 where as 3*2 = 6)
   b) Q(4) - true    (2^4 = 16 where as 3*4 = 12)
   c) true   (it is because for x < 4 (positive numbers) Q(x) is false and for x > 4, Q(x) is true
   d) true   (if we take x = -1)

3. a) All students who have taken discrete match, understabds boolean algebra

   b) There are some students who know boolean algebra and they have not
      taken discrete math.

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