Suppose that ? = {2, 4, 6}, ? = {2, 6}, ? = {4, 6} ??? ? = {4, 6, 8}. Determine which of these sets are subsets of the other sets. b. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. i. f(a) = b, f(b) = a, f(c) = c, f(d) = d ii. f(a) = b, f(b) = b, f(c) = d, f(d) = c iii. f(a) = d, f(b) = b, f(c) = c, f(d) = d c. Write in symbols: ′??? ??? ?, ? < 5 ?? ? ≥ 5′ d. Express the following propositions in symbolic form, and identify the principal connective: i. Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is studying mathematics. ii. It is not the case that if it is sunny then I will carry an umbrella.
Suppose that ? = {2, 4, 6}, ? = {2, 6}, ? = {4, 6} ??? ? = {4, 6, 8}. Determine which of
these sets are subsets of the other sets.
b. Determine whether each of these functions from {a, b, c, d} to itself is one-to-one.
i. f(a) = b, f(b) = a, f(c) = c, f(d) = d
ii. f(a) = b, f(b) = b, f(c) = d, f(d) = c
iii. f(a) = d, f(b) = b, f(c) = c, f(d) = d
c. Write in symbols: ′??? ??? ?, ? < 5 ?? ? ≥ 5′
d. Express the following propositions in symbolic form, and identify the principal connective:
i. Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is
studying mathematics.
ii. It is not the case that if it is sunny then I will carry an umbrella.
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