Question

Based on the given statement, two conclusions are drawn. Find out which conclusion is true based on the statement.

Statement:

A < Q, \, Q \leq X, \, E = A < T

Conclusions:

1. T < E

2. $A = X$

• A. Both conclusions 1 and 2 are true
• B. Only conclusion 2 is true
• C. Only conclusion 1 is true
• D. Neither conclusion 1 nor 2 is true

Answer 1

Answer:

D. Neither conclusion 1 nor 2 is true

Neither conclusion is true (both are false).

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First, let's combine the separate inequalities given in the statement into logical chains.

• Given parts:

  1. E = A < T

  2. A < Q \leq X

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Evaluating Conclusion 1: T < E

• From the statement E = A < T, we know directly that E < T.

• Therefore, the reverse statement T < E is completely contradictory and false.

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Evaluating Conclusion 2: $A = X$

• From the chain A < Q \leq X, we can follow the inequality signs from $A$ to $X$:

  • Since $A$ is strictly less than $Q$ (A < Q), and $Q$ is less than or equal to $X$ ($Q \leq X$), it means $A$ must be strictly less than $X$.

  • This gives the relationship: A < X.

• Because $A$ is strictly smaller than $X$, it can never be equal to $X$. Thus, $A = X$ is false.