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    Coded Ineqaulities

    Question

    In the following questions, the symbols α, β, Ώ, ¥ and £ are used with the following meaning as illustrated below.

    ‘P α Q’ means ‘P is greater than Q’

    ‘P β Q’ means ‘P is either greater than or equal to Q’

    ‘P Ώ Q’ means ‘P is equal to Q’

    ‘P ¥ Q’ means ‘P is smaller than Q’

    ‘P £ Q’ means ‘P is either smaller than or equal to Q’

    Now in each of the following the questions assuming the given statements to be true, find which of the two conclusions I and II given below is/are definitely true?

    Give answer

    a): If only conclusion I is true.

    b): If only conclusion II is true.

    c): If either conclusion I or II is true.

    d): If neither conclusion I nor II is true.

    e): If both conclusions I and II are true.

    Statements: R β S, O £ P, P ¥ S

    Conclusions:

    I. R α O

    II. P £ R

    A If only conclusion I is true. Correct Answer Incorrect Answer
    B If only conclusion II is true. Correct Answer Incorrect Answer
    C If either conclusion I or II is true. Correct Answer Incorrect Answer
    D If neither conclusion I nor II is true. Correct Answer Incorrect Answer
    E If both conclusions I and II are true. Correct Answer Incorrect Answer

    Solution

    Given statement: R β S, O £ P, P ¥ S   Decoded statement: R ≥ S, O ≤ P, P < S Combined statement: R ≥ S > P ≥ O Conclusion I - R α O, R > O, it is true. Conclusion II- . P £ R, R ≥ P, it is not true.

    Question

    Statements: F ¥ Z, H β A, F α H

    Conclusions:

    I. Z β A

    II. A £ F

    A If only conclusion I is true. Correct Answer Incorrect Answer
    B If only conclusion II is true. Correct Answer Incorrect Answer
    C If either conclusion I or II is true. Correct Answer Incorrect Answer
    D If neither conclusion I nor II is true. Correct Answer Incorrect Answer
    E If both conclusions I and II are true. Correct Answer Incorrect Answer

    Solution

    Given statement: F ¥ Z, H β A, F α H Decoded statement: F < Z, H ≥ A, F > H Combined statement:   A ≤ H < F < Z   Conclusion I - Z β A, Z ≥ A, it is not true Conclusion II - A £ F, A ≤ F, it is not true.

    Question

    Statements: O ¥ R, U α V, O β V

    Conclusions:

    I. U Ώ O

    II. V ¥ R

    A If only conclusion I is true. Correct Answer Incorrect Answer
    B If only conclusion II is true. Correct Answer Incorrect Answer
    C If either conclusion I or II is true. Correct Answer Incorrect Answer
    D If neither conclusion I nor II is true. Correct Answer Incorrect Answer
    E If both conclusions I and II are true. Correct Answer Incorrect Answer

    Solution

    Given statement: O ¥ R, U α V, O β V Decoded statement: O < R, U > V, O ≥ V Combined statement: U > V ≤ O < R Conclusion I - U Ώ O, U = O, it is not true Conclusion II - V ¥ R, V < R, it is true.

    Question

    Statements: W Ώ X, Z α Y, W ¥ Y

    Conclusions:

    I. Y Ώ X

    II. W ¥ Z

    A If only conclusion I is true. Correct Answer Incorrect Answer
    B If only conclusion II is true. Correct Answer Incorrect Answer
    C If either conclusion I or II is true. Correct Answer Incorrect Answer
    D If neither conclusion I nor II is true. Correct Answer Incorrect Answer
    E If both conclusions I and II are true. Correct Answer Incorrect Answer

    Solution

    Given statement: W Ώ X, Z α Y, W ¥ Y Decoded statement: W = X, Z > Y, W < Y Combined statement: Z > Y > W = X Conclusion I - Y Ώ X, Y = X, it is not true. Conclusion II - W ¥ Z, W < Z, it is true.

    Question

    Statements: I α J, L £ M, J Ώ M

    Conclusions:

    I. J α L

    II. L Ώ J

    A If only conclusion I is true. Correct Answer Incorrect Answer
    B If only conclusion II is true. Correct Answer Incorrect Answer
    C If either conclusion I or II is true. Correct Answer Incorrect Answer
    D If neither conclusion I nor II is true. Correct Answer Incorrect Answer
    E If both conclusions I and II are true. Correct Answer Incorrect Answer

    Solution

    Given statement: I α J, L £ M, J Ώ M   Decoded statement: I > J, L ≤ M, J = M Combined statement: I > J = M ≥ L Conclusion I - J α L, J > L, it can be true. Conclusion I - L Ώ J, L = J, it can be true.