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1.  
Statement: P > Q ≥ R = S. What is the strongest relation between P and S that is definitely true?

Correct Answer: B [P > S]

Explanation:

P > Q ≥ R = S → P > S.

2.  
Statement: M ≤ N < O = T. What is the strongest relation between M and T that is definitely true?

Correct Answer: A [M < T]

Explanation:

M ≤ N < O = T → M < T.

3.  
Statement: A ≥ B ≤ C. What is the strongest relation between A and C that is definitely true?

Correct Answer: C [No definite relation]

Explanation:

A ≥ B ≤ C – signs oppose, so no definite relation.

4.  
Statements: K > L, L ≥ M, M = N. The conclusion "K > N" is:

Correct Answer: A [Definitely true]

Explanation:

K > L ≥ M = N – one strict sign and no opposite sign, so K > N is definitely true.

5.  
Statements: U ≤ V < W, X > W. The conclusion "U ≥ X" is:

Correct Answer: B [Definitely false]

Explanation:

U ≤ V < W < X gives U < X, so U ≥ X can never be true – definitely false.

6.  
Statements: G ≥ H, H = J, J ≤ K. The conclusion "G > K" is:

Correct Answer: C [May be true, but not definite]

Explanation:

G ≥ H = J ≤ K – signs oppose at J, so G > K is possible but not certain.

7.  
Fill in the blank: which sign in place of ? makes "B > E" definitely true in B ≥ C ? D = E?

Correct Answer: D [>]

Explanation:

B ≥ C needs one strict sign after it; only > gives B > E (≥ or = give only B ≥ E).

8.  
Which sign can replace ? in H < I ? J ≤ K so that both "H < K" and "I ≤ K" are definitely true?

Correct Answer: C [=]

Explanation:

Among the options only = works: H < I = J ≤ K gives H < K and I ≤ K; > or ≥ break the chain.

9.  
Statements: A ≥ B > C
Conclusions: I. A > C II. C ≥ A

Correct Answer: A [Only I follows]

Explanation:

I: A ≥ B > C – true; II: C < B ≤ A gives C < A, so C ≥ A is false

10.  
Statements: F < G, G ≤ H, J > H
Conclusions: I. F ≥ J II. G < J

Correct Answer: B [Only II follows]

Explanation:

I: F < G ≤ H < J gives F < J, so F ≥ J is false; II: G ≤ H < J – true

11.  
If '@' means '≥', '#' means '<', '$' means '=' and '%' means '>', then "P @ Q # R $ S" means:

Correct Answer: B [P ≥ Q < R = S]

Explanation:

Replace each symbol: @ → ≥, # → <, $ → =.

12.  
From A > B = C ≥ D, which of the following does NOT follow?

Correct Answer: D [A = D]

Explanation:

A > B = C ≥ D gives A > D, so A = D is false; the other three are true.

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