Predicates and Quantifiers

Let P(x), Q(x) and R(x) be statements "x is a clear explanation", "x is satisfactory" and "x is an excuse" respectively. Suppose that the universe of discourse for x consists of all English test. Express the following statements using quantifiers, logical connectives and P(x), Q(x) and R(x) a) All clear explanations are satisfactory b) some excuses are satisfactory c)some excuses are not clear explanations d) does (c) follow from (a) and (b) ? (explain)

Discrete Mathematics Problems

Discrete Mathematics Problems. See attached file for full problem description.

Discrete Mathematics Problems

1. Let A = {1, 2, 3, 4}, B = {3, 4, 5}, C = {1}, and D = {x: 3 < x < 10}. Are each of the following true or false? b. B ⊆ D c. ∅ ⊆ D 2. Calculate the following: a. P(8, 4) 3. Let A = {1, 2, 3, 4}, B = {1, 4, 5}, C = {3, 5, 6}, and the universal set U = {1, 2, 3, 4, 5, 6}. a. Determine the resulting set: b. Determine the resulting set: 4. Determine which of the reflexive, symmetric, and transitive properties are satisfied by the given relation R defined on set S, and state whether R is an equivalence relation on S. a. S = {1,2,3,4,5,6,7,8} and x R y means that x - y = 0 b. S = {1,2,3,4,5,6,7,8} and x R y means that x > y 5.... click for more