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Inequalities - Intermediate Level: inequality logic INTERMEDIATE

Master inequalities concepts through this excellence pursuit practice set. Worksheet 16 of 30 contains 20 intermediate-level problems. Deep dive into inequality logic while learning comparative reasoning, mathematical inequalities, symbolic inequalities. Recommended for mid-level learners aiming for moderate complexity with mixed patterns.

📝 Worksheet 16 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 16 of 30 (53% complete)

Question 1

Statements: B ≥ D > G ≥ C Conclusion: C > B Is the conclusion true?
From B ≥ D > G ≥ C, C > B contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 2

Statement: S = Q > N ≥ R > M Which conclusions are definitely true?
From S = Q > N ≥ R > M, we can derive: Q > R, N > M. These conclusions definitely follow.
multiple, evaluation, analysis

Question 3

Statements: I. E < F > A II. F ≤ C < D Which conclusion is definitely false?
From the statements, E > D contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 4

Statements: A > F > H > E Conclusion: F = E Is the conclusion true?
From A > F > H > E, we cannot determine the exact relationship between F and E.
basic, comparison, transitive

Question 5

Statements: V > U ≥ T; Q ≤ T < W; W = S; S ≥ R Which of the following is definitely true?
Analyzing the chain: V > U ≥ T; Q ≤ T < W; W = S; S ≥ R. Therefore, W ≥ R is definitely true.
complex, chain, multi-step

Question 6

Statements: I. D > C ≥ G II. G = F > A Which conclusions definitely follow?
Combining statements: D > C ≥ G = F > A. Therefore, I, II, and III definitely follow(s).
compound, multiple, chain

Question 7

Statements: I. B < C > F II. C ≤ D < E Which conclusion is definitely false?
From the statements, B > E contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 8

Statement: M = R > S ≥ Q > O Which conclusions are definitely true?
From M = R > S ≥ Q > O, we can derive: R > Q, S > O. These conclusions definitely follow.
multiple, evaluation, analysis

Question 9

Statement: W ≥ X ≥ Y Conclusions: I. W > Y II. W = Y Which follows?
From W ≥ X ≥ Y, either W > Y or W = Y. Hence either I or II follows.
either-or, logical, possibility

Question 10

Statement: W ≥ X ≥ Y Conclusions: I. W > Y II. W = Y Which follows?
From W ≥ X ≥ Y, either W > Y or W = Y. Hence either I or II follows.
either-or, logical, possibility

Question 11

Statement: W ≤ X ≤ Z Conclusions: I. W < Z II. W = Z Which follows?
From W ≤ X ≤ Z, either W < Z or W = Z. Hence either I or II follows.
either-or, logical, possibility

Question 12

Statements: H > B = E > D Conclusion: D > H Is the conclusion true?
From H > B = E > D, D > H contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 13

Directions: ! means >, ^ means ≤, ? means <, * means ≥, ~ means = Statement: R ? P * T ^ Q Which conclusion follows?
Decoding: R < P → < P ≥ T → ≥ T ≤ Q. Therefore, No definite conclusion.
coded, symbols, decoding

Question 14

Statement: N ≥ O > R = S ≥ Q Which conclusions are definitely true?
From N ≥ O > R = S ≥ Q, we can derive: N > R. These conclusions definitely follow.
multiple, evaluation, analysis

Question 15

Statements: I. D ≥ A > C II. C < B ≤ E Which conclusion is definitely false?
From the statements, D < E contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 16

Statements: G > D > F ≥ H Conclusion: H > G Is the conclusion true?
From G > D > F ≥ H, H > G contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 17

Statements: I. B > E ≥ A II. A = D > F Which conclusions definitely follow?
Combining statements: B > E ≥ A = D > F. Therefore, I, II, and III definitely follow(s).
compound, multiple, chain

Question 18

Arrange the elements A, E, C, B, D based on these clues: - B > D - C > B - C < E - A > E Which element is the largest?
From the clues: A > E > C > B > D. Therefore, A is the largest.
puzzle, arrangement, ordering

Question 19

Statements: D ≥ E ≥ F > G Conclusion: G > D Is the conclusion true?
From D ≥ E ≥ F > G, G > D contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 20

Statements: I. F < A > C II. A ≤ D < E Which conclusion is definitely false?
From the statements, F > E contradicts the established relationships and is definitely false.
reverse, mixed, direction
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