Question

In usual notations prove that (A U B) U C = A U (B U C)​

Answer 1

Answer:

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Step-by-step explanation:

using the information given below do not add many do you have the following conversation with the speaker

Answer 2

SOLUTION

TO PROVE

In usual notations prove that

(A U B) U C = A U (B U C)

PROVE

Let x ∈ ( A U B ) U C

⟹ x ∈ ( A ∨ B ) ∨ C

⟹ x ∈ A ∨ B ∨ C

⟹ x ∈ A ∨ ( B ∨ C )

⟹ x ∈ A U (B U C)

∴ (A U B) U C ⊆ A U (B U C) - - - - - - - (1)

Let y ∈ A U ( B U C )

⟹ y ∈ A ∨ ( B ∨ C )

⟹ y ∈ A ∨ B ∨ C

⟹ y ∈ ( A ∨ B ) ∨ C )

⟹ y ∈ ( A U B ) U C

∴ A U (B U C) ⊆ (A U B) U C - - - - - - - (2)

From (1) & (2) we get

(A U B) U C = A U (B U C)

Hence proved

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