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​​​​​​​Consider the sentence below:

“There is a country that borders both India and Nepal”

Which of the following represents the above sentence correctly?

  1. $\exists c \text{ Country} (c ) \wedge \text{Border}(c, \text{India}) \wedge Border(c, \text{Nepal})$
  2. $\exists c \text{ Country} (c ) \Rightarrow [\text{Border}(c, \text{India}) \wedge Border(c, \text{Nepal})]$
  3. $[\exists c \text{ Country} (c ) ] \Rightarrow [\text{Border}(c, \text{India}) \wedge Border(c, \text{Nepal})]$
  4. $\exists c \text{ Border}( \text{Country} (c ), \text{India} \wedge \text{Nepal})$
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It is a boolean logic:

Either there will be such country (1) or no such country (0).

We are having two variables; India and Nepal.

The AND operation will result TRUE only if Border(c,India) is (1) and Border(c,Nepal) is (1).

And if we are having 1 from last two variables, the only case that give TRUE(1) is when we are having AND with Country(1).

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