T
or F and explanation
Please write clearly,thank you
1. A ∩ ∅ = A
2....
T
or F and explanation
Please write clearly,thank you
1. A ∩ ∅ = A
2. The number of (ordered) lists of r objects chosen from n is
C(n, r)
3. P(n, r) ≥ C(n, r)
4. If A and B are finite sets, then n(A × B) = n(A) ×
n(B)
5. If A and B are finite sets, then n(A ∩ B) = n(A) + n(B) −
n(A ∪ B)
T
or F and explanation
1.There are 5! possible sets of five specific names.
2. A...
T
or F and explanation
1.There are 5! possible sets of five specific names.
2. A ∪ A ′ = ∅
3. If A and B are finite sets, then n(A ∪ B) = n(A) +
n(B)
4. C(10, 9) = C(10, 1)
5. If A and B are finite sets, then n(A ∪ B) = n(A) + n(B) −
n(A ∩ B)
Relations and Functions
Usual symbols for the above are;
Relations: R1, R2, S, T, etc
Functions:...
Relations and Functions
Usual symbols for the above are;
Relations: R1, R2, S, T, etc
Functions: f, g, h, etc. But remember a function is a special
kind of relation so it might turn out that a Relation, R, is a
function, too.
Relations
To understand the symbolism better, let’s say the domain of a
relation, R, is A = { a, b , c} and the Codomain is B = {
1,2,3,4}.
Here is the relation: a R 1, ...
Identify whether the following are true or false. (a) 5 ∈ {1, 2,
{3, 4}, {1},...
Identify whether the following are true or false. (a) 5 ∈ {1, 2,
{3, 4}, {1}, {5}} (b) {5} ∈ {1, {2}, {3, 4}, 5, {5}} (c) {5} ⊆ {1,
{2}, {3, 4}, 5, {5}} (d) {3, 4} ⊆ {1, 2, {3, 4}, {1}, {5}} (e) {1,
2} ⊆ {1, 2, {3, 4}, {1}, {5}} (f) {5} ∈ P(N) (g) {5} ⊆ P(N) (h)
{{5}} ∈ P(N) (i) ∅ ⊆ P(R) (j) ∅ ∈ P(R)
Determine the number of ordered pairs (A, B), where A ⊆ B ⊆ {1,
2, ....
Determine the number of ordered pairs (A, B), where A ⊆ B ⊆ {1,
2, . . . , n}