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An amphoteric substance is:
A.A substance that can act as both acids and base by being both proton acceptor and proton donor.
B.A substance that acts as an acid by being both a proton acceptor and a proton donor
C.A substance that acts as a base be being both a proton acceptor and a proton donor
D.When a hydronium ion from a base reacts with a hydroxide ion from an acid to make water and a salt
E.A base that forms when an acid loses a proton.

Answer
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Hint: Acids are substances that can donate hydrogen ion to bases and hydrogen ion is a proton. So, we can say that acid is a proton donor. Similarly, bases are substances that accept these protons and therefore, they can be referred to as proton acceptors.

Complete step by step answer:
 A substance that can act as a proton donor or proton acceptor is called as amphiprotic substances. This can also be defined as amphoteric substances which acts as acid as well as base. The most common example we come across every day in our life is water which is amphoteric in nature.
A Hydrogen atom has one proton and one electron. Technically a hydrogen ion is just a proton, made by removal of an electron from it. So, we call an acid a proton donor and base as a proton acceptor. And such a reaction between an acid and a base is essentially a proton transfer reaction.
In case of water, we can also call it an auto-ionisation of water. It means that one water molecule can react with another to form hydroxide ion and hydronium ion while auto-ionising.
 \[2{H_2}O(l) \rightleftharpoons {H_3}{O^ + }(aq) + O{H^ - }(aq)\]
In this reaction we can clearly say that water itself acts as a proton donor and proton acceptor. So, it is an amphoteric substance. Thus, an amphoteric substance is a substance that can act as both acids and base by being both proton acceptor and proton donor.

Hence, the correct option is (A).

Note:
The Arrhenius definition of an acid states that acid is a substance that dissociates in water to produce protons and Arrhenius base is a substance that dissociates to produce hydroxide ions in water. This tells us that these two ions can combine to form water.