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Home » Determine whether each of the statement in Exercise for all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C, is true or false. Justify your answer.
Determine whether each of the statement in Exercise for all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C, is true or false. Justify your answer.
CBSE | Class 11 | Maths | NCERT Exemplar | Sets
Determine whether each of the statement in Exercise for all sets A, B and C, if A ⊂ B, then A ∪ C ⊂ B ∪ C, is true or false. Justify your answer.

Solution:

The statement is true

As per the question,

Three sets are A, B and C

We need to check: if A \subset B, therefore A \cup C \subset B \cup C is true or false

Let’s say x \in A \cup C

\begin{array}{l} \Rightarrow \mathrm{x} \in \mathrm{A} \text { or } \mathrm{x} \in \mathrm{C} \\ \Rightarrow \mathrm{x} \in \mathrm{B} \text { or } \mathrm{x} \in \mathrm{C}\{\because \mathrm{A} \subset \mathrm{B}\} \\ \Rightarrow \mathrm{x} \in \mathrm{B} \cup \mathrm{C} \\ \Rightarrow \mathrm{A} \cup \mathrm{C} \subset \mathrm{B} \cup \mathrm{C} \end{array}

As a result, the provided statement “for all sets A, B and C, if A \subset B, therefore A \cup C \subset B \cup C ” is true

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