Question

Show that (A – B) – C = (A – C) – (B – C)​

Answer 1

Answer:

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Step-by-step explanation:

India, officially the Republic of India (Hindi: Bhārat Gaṇarājya),[23] is a country in South Asia. It is the second-most populous country, the seventh-largest country by land area, and the most populous democracy in the world. Bounded by the Indian Ocean on the south, the Arabian Sea on the southwest, and the Bay of Bengal on the southeast, it shares land borders with Pakistan to the west;[f] China, Nepal, and Bhutan to the north; and Bangladesh and Myanmar to the east. In the Indian Ocean, India is in the vicinity of Sri Lanka and the Maldives; its Andaman and Nicobar Islands share a maritime border with Thailand, Myanmar and Indonesia.

Answer 2

Answer:

(A – B) – C = (A – C) – (B – C)

Step-by-step explanation:

Just follow the definition.We define:

A−B={x∈U;x∈A∧x∉B}

Thus write left side of the equation:

(A−B)−C={x∈U;x∈(A−B)∧x∉C} ={x∈U;x∈A∧x∉B∧x∉C}

Now let's write the right side:

(A−C)−(B−C)=

{x∈U;x∈(A−C)∧x∉(B−C)}=

{x∈U;(x∈A∧x∉C) ∧(x∉B∧x∉C)}=

={x∈U;x∈A∧x∉B∧x∉C}

When you compare these two sets, they are the same. Q.E.D.