3. Determine which of the following symbols: Cóz makes the premise true. a. {b} {a, b} b. 1__ {1, 2, 3} c. Ø {a, b, c, d} d. IfA = {1, 2, 3, 4, 5} y B = {1, 3, 5}, Then, A_B e. Si A = {1, 2, 3, 4, 5} y B = {1, 3, 5}, entonces, {1, 2, 3, 5} _B
3. Determine which of the following symbols: Cóz makes the premise true. a. {b} {a, b} b. 1__ {1, 2, 3} c. Ø {a, b, c, d} d. IfA = {1, 2, 3, 4, 5} y B = {1, 3, 5}, Then, A_B e. Si A = {1, 2, 3, 4, 5} y B = {1, 3, 5}, entonces, {1, 2, 3, 5} _B
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Determine which of the following symbols: Cóz makes the premise true.
a. {b}
{a, b}
b. 1__ {1, 2, 3}
c. Ø
{a, b, c, d}
d. IfA = {1, 2, 3, 4, 5} y B = {1, 3, 5}, Then, A_B
e. Si A = {1, 2, 3, 4, 5} y B = {1, 3, 5}, entonces, {1, 2, 3, 5} _B
Expert Solution
Part a)
Given:
{b} ______ {a, b}
The symbol ⊆ means a subset of A⊆B, that is, each element of A is an element of B.
If any or none of the elements of A is not in B, then it is shown as A ⊈ B.
As b∈{a, b} is contained in that is {b} is contained in {a, b}.
Therefore, {b} ⊆ {a, b}.
Part b)
Given:
1 ______ {1, 2, 3}
As 1 is an element not set, therefore, 1∈ {1, 2, 3} but 1⊈{1, 2, 3}.
Part c)
Given:
Ø __________ {a, b, c, d}.
The empty set is denoted by Ø.
As the empty set is a subset of every set.
Thus Ø ⊆ {a, b, c, d}.
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