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
Directions: A statement is given followed by two inferences I and II. You have to consider the statement to be true even if it seems to be at variance with commonly known facts. You have to decide which of the given inferences, if any, follow from the given statement.
Statement: Many students are addicted to mobile games and this leads to poor academic performance.
Inference:
I. Many Students are not paying attention to studies due to mobile games.
II. It is only because of mobile games that students fail in the examination.
'Little knowledge is a dangerous thing' is a decision based on:
It is better to spend the leftovers after saving. Financial discipline and self-control can make you rich. Saving money after spending is not a good habit. Which among the following statements is true as per the statement?
A. If you spend first then you will be spendy.
B. If you save before spending, you will become rich.
C. If you spend before saving, you will be poor.
D. Saving by borrowing is a bad habit.
Which of the following is the assumption for the claim that 'Pleasure is desirable'?
Read the given statements carefully and answer the questions.
Fear of danger is more dangerous than danger itself. Risk is directly proportional= to danger
Which of the following are true according to the given statements?
A. Fear is worse than any fearful threat.
B. There is a trade-off between risk and danger.
C. There should be fear of danger.
D. There is no need to take risks to overcome any danger.
