TIFR CSE 2014 | Part A | Question: 8

Question

All that glitters is gold. No gold is silver.

Claims:

1. No silver glitters.
2. Some gold glitters.

Then, which of the following is TRUE?

• A. Only claim $1$ follows.
• B. Only claim $2$ follows.
• C. Either claim $1$ or claim $2$ follows but not both.
• D. Neither claim $1$ nor claim $2$ follows.
• E. Both claim $1$ and claim $2$ follow.

Answer 1

Lets simplify this by another example.

1.All scientists are Human.--------------------every x in universe if x is scientist then x is human.----∀x:(scientist(x)⟹ Human(x))

2.No  human is Dog.-------------------------¬∃x:(human(x)∧ Dog(x))

claims:-

1.No dog is scientist.----------For this to be false ,some dog should be scientist but scientist if exist are only humans and no human is dog hence above statement is true.

2.some human are scientist.----every scientist if exists is human,but if there are no scientists .then no human is scientist.Hence this is false.