Assume that a ∈ A, where A is a set. Which of these statements are true and which are false, where all sets shown are ordinary sets, and not multisets. Explain each answer.a) {a, a} ∪ {a, a, a} = {a, a, a, a, a}b) {a, a} ∪ {a, a, a} = {a}c) {a, a} ∩ {a, a, a} = {a, a}d) {a, a} ∩ {a, a, a} = {a}e) {a, a, a} − {a, a} = {a}
Assume that a ∈ A, where A is a set. Which of these statements are true and which are false, where all sets shown are ordinary sets, and not multisets. Explain each answer.a) {a, a} ∪ {a, a, a} = {a, a, a, a, a}b) {a, a} ∪ {a, a, a} = {a}c) {a, a} ∩ {a, a, a} = {a, a}d) {a, a} ∩ {a, a, a} = {a}e) {a, a, a} − {a, a} = {a}
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 38SE: Suppose a set A has 2,048 subsets. How many distinct objects are contained in A?
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Assume that a ∈ A, where A is a set. Which of these statements are true and which are false, where all sets shown are ordinary sets, and not multisets. Explain each answer.
a) {a, a} ∪ {a, a, a} = {a, a, a, a, a}
b) {a, a} ∪ {a, a, a} = {a}
c) {a, a} ∩ {a, a, a} = {a, a}
d) {a, a} ∩ {a, a, a} = {a}
e) {a, a, a} − {a, a} = {a}
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