Select the correct alternative from the given choices. If B ⊇A and C ⊆A, then which of the follo

Name: Problem 11, Chapter 4: Computer Science and Information Technology
Uploaded: 2022-01-23T19:11:44-08:00
Duration: 1 min 51 s
Channel: Muhammad Nawaz
Description: Select the correct alternative from the given choices. If B ⊇A and C ⊆A, then which of the following is necessarily true? (A) B ⊆C (B) B=C (C) A=B ≠C (D) C ⊆B

step 1 Hello students our question is if B is super set of a and C is subset of a then which of the fol

Question

Select the correct alternative from the given choices. If $\mathrm{B} \supseteq \mathrm{A}$ and $\mathrm{C} \subseteq \mathrm{A}$, then which of the following is necessarily true? (A) $\mathrm{B} \subseteq \mathrm{C}$ (B) $\mathrm{B}=\mathrm{C}$ (C) $\mathrm{A}=\underline{\mathrm{B}} \neq \mathrm{C}$ (D) $C \subseteq B$

   Select the correct alternative from the given choices.
If $\mathrm{B} \supseteq \mathrm{A}$ and $\mathrm{C} \subseteq \mathrm{A}$, then which of the following is necessarily true?
(A) $\mathrm{B} \subseteq \mathrm{C}$
(B) $\mathrm{B}=\mathrm{C}$
(C) $\mathrm{A}=\underline{\mathrm{B}} \neq \mathrm{C}$
(D) $C \subseteq B$

Computer Science and Information Technology

Trishna Knowledge… 2018 Edition

Chapter 4, Problem 11

Instant Answer

Solved by Expert Muhammad Nawaz

01/23/2022

Step 1

This means that all elements of set A are also in set B and all elements of set C are also in set A. Show more…

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Select the correct alternative from the given choices. If $\mathrm{B} \supseteq \mathrm{A}$ and $\mathrm{C} \subseteq \mathrm{A}$, then which of the following is necessarily true? (A) $\mathrm{B} \subseteq \mathrm{C}$ (B) $\mathrm{B}=\mathrm{C}$ (C) $\mathrm{A}=\underline{\mathrm{B}} \neq \mathrm{C}$ (D) $C \subseteq B$

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Key Concepts

Subset and Superset Relationships

This concept involves understanding the definitions of subsets and supersets. A set X is considered a subset of Y (denoted X ? Y) if every element of X is also an element of Y, and conversely, Y is a superset of X (denoted Y ? X). These relationships are fundamental in set theory and are used to compare the elements of different sets.

Transitive Property of Subset Relations

The transitive property in set theory states that if one set is a subset of a second set, and the second set is in turn a subset of a third set, then the first set is also a subset of the third. Formally, if C ? A and A ? B, it implies that C ? B. This property is crucial for deducing relationships between sets when multiple subset or superset conditions are given.

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