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 comes home, she brings sweet A. she came home B. she did not come home C. she brought sweet D. she did not bring sweet
AC
Understanding the Main Statement
The main statement is: "When she comes home, she brings sweet." This is a conditional statement, which can be represented in logic as:
Let P be the statement "She comes home."
Let Q be the statement "She brings sweet."
The main statement translates to: If P, then Q. Mathematically, this is written as $P \implies Q$.
This means that *if* she comes home, it is guaranteed that she also brings sweet. It doesn't say anything about what happens if she *doesn't* come home.
Analyzing the Provided Statements
- Statement A: "she came home" represents P.
- Statement B: "she did not come home" represents $\neg P$ (Not P).
- Statement C: "she brought sweet" represents Q.
- Statement D: "she did not bring sweet" represents $\neg Q$ (Not Q).
Evaluating the Option Pairs
We need to find an ordered pair (first statement implies second) where both statements are logically consistent with the main statement ($P \implies Q$).
Option 1: BA
This pair means: "She did not come home" (B) implies "She came home" (A). In logical terms: $\neg P \implies P$. This is a logical contradiction and is false. Therefore, this option is incorrect.
Option 2: DA
This pair means: "She did not bring sweet" (D) implies "She came home" (A). In logical terms: $\neg Q \implies P$. From the main statement ($P \implies Q$), we know its contrapositive is $\neg Q \implies \neg P$ ("If she did not bring sweet, then she did not come home"). The statement $\neg Q \implies P$ contradicts the contrapositive and is not necessarily true based on the main statement. Therefore, this option is incorrect.
Option 3: AC
This pair means: "She came home" (A) implies "She brought sweet" (C). In logical terms: $P \implies Q$. This implication is exactly the main statement itself. If statement A (P) is true, the main statement ($P \implies Q$) directly tells us that statement C (Q) must also be true. Both statements A (P) and C (Q) are components of the main conditional statement and are consistent with it. This fulfills both conditions: the first implies the second, and both are logically consistent with the main statement. Therefore, this is the correct option.
Option 4: CD
This pair means: "She brought sweet" (C) implies "She did not bring sweet" (D). In logical terms: $Q \implies \neg Q$. This is a logical contradiction and is false. Therefore, this option is incorrect.
Conclusion
The only ordered pair of statements that satisfies the conditions is AC, as it directly reflects the logic of the main statement "When she comes home, she brings sweet."
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?
