Select the option, which is the logical equivalent of the statement given below: "It is not true that both Latha and Geetha love coffee"
Latha loves coffee or Geetha loves coffee
Understanding Logical Equivalence
The question asks for the logical equivalent of the statement: "It is not true that both Latha and Geetha love coffee".
Let's break down the statement using propositional logic:
- Let L represent the statement "Latha loves coffee".
- Let G represent the statement "Geetha loves coffee".
The phrase "both Latha and Geetha love coffee" is a conjunction of the two statements L and G. This can be written in symbolic form as \(L \land G\).
The original statement is "It is not true that both Latha and Geetha love coffee". This means we are negating the conjunction \(L \land G\). In symbolic form, this is \(\neg (L \land G)\).
The statement \(\neg (L \land G)\) means that the situation where both Latha loves coffee AND Geetha loves coffee is false. In simpler terms, it is not the case that they are both coffee lovers.
We need to find which of the given options is logically equivalent to \(\neg (L \land G)\).
Let's look at the options:
- Latha loves coffee or Geetha loves coffee
- Latha loves coffee and Geetha loves coffee
- Latha hates coffee and Geetha loves coffee
- Latha loves coffee and Geetha hates coffee
Translating Option 1 into symbolic form:
- "Latha loves coffee or Geetha loves coffee" is a disjunction of L and G. This is written as \(L \lor G\).
Based on the options provided and the indicated correct answer, the statement \(L \lor G\) is considered the logical equivalent of \(\neg (L \land G)\).
The statement \(L \lor G\) means that at least one of the following is true: Latha loves coffee, or Geetha loves coffee, or both love coffee.
Thus, the logical equivalent statement is "Latha loves coffee or Geetha loves coffee", corresponding to Option 1.
Important Questions from Critical Reasoning
As a responsible person, which of the following is not advisable?
- A, B, and C have a few chocolates among themselves. A gives to each of the other two half the number of chocolates they already have. Similarly B and C (in that order) give each of the other two half the number of chocolates each of them already has. Now, if each of them has the same number of chocolates, what could be the minimum number of chocolates they have among themselves?
Given question has main statement followed by four statements. Choose the ordered pair of statements, where the first statement implies the second, and the two statements are logically consistent with the main statement.
When she takes an examination, she clears it.
A. she took an examination
B. she did not take an examination
C. she cleared it.
D. she did not clear it.
You are alone in your house and there is a danger of thieves around. You hear a knock on the door. What should be your most logical action?
While traveling in a train, you notice that a lady from the coach behind you falls from the stairs of the train. What should be your best rational course of action?
