Discrete Mathematics Answers

Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find

a. (A ∪ B) ∩ C.

b. (A ∩ B) ∪ C.

c. (A ∪ B) ∩ (A ∪ C).

Identify if the given statement is a proposition or not.

There are no black flies in Maine.

Write down all derangements of the set \left\{ a,b,c,d \right\} and show that the number of derangements is the same as predicted by the recurrence D(n) = (n - 1)(D(n - 2) + D(n - 1)) with initial values D(1) = 0 and D(2) = 1. Hint: a derangement is a permutation of an ordered set where no element is in the same place as before. Example: \left\{ b,a,d,c \right\} is a derangement of \left\{ a,b,c,d \right\} because all of the letters positions have changed.

How can I use a venn diagram to represent (1,2,3,4,5) and (1,3,5)

What is the cardinality of each of these sets?

a. {a}

b. {{a}}

c. {a,{a}}  

d. {a,{a},{a,{a}}}  

e. {∅,{∅},{∅,{∅}}} 

“If compound X is boiling, then its temperature must be at least 150◦C.” Assuming that this

statement is true, which of the following must also be true?

a. If the temperature of compound X is at least 150◦C, then compound X is boiling.

b. If the temperature of compound X is less than 150◦C, then compound X is not boiling.

c. Compound X will boil only if its temperature is at least 150◦C.

d. If compound X is not boiling, then its temperature is less than 150◦C.

e. A necessary condition for compound X to boil is that its temperature be at least 150◦C.

f. A sufficient condition for compound X to boil is that its temperature be at least 150◦C.

How many assignments of truth values to p; q; r and w are there for which

((p → q) → r) → w is true? Guess a formula in terms of the number of variables.

Find the counter example, if possible to these universally quantified statements,where the domain for all variables consists of all integers.

Ax (x > 0 V x < 0)