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Logical Reasoning :: Symbols and Notations

  1. a + b means a is neither less than nor equal to b.
    a - b means a is neither smaller nor greater than b.
    a = b means a is not less than b.
    a * b means a is not greater than b.
    a / b means a is neither greater than nor equal to b.

    Statements:           P + Q, Q - R, R + S
    Conclusions:          I. P = S
                                  II. P / R
  2. A.
    if only conclusion (I) follows
    B.
    if only conclusion (II) follows
    C.
    if both conclusions (I) and (II) follows
    D.
    if neither (I) nor (II) follows
    E.
    if either conclusion (I) or (II) follows

  3. a £ b means a is less than or equal to b.
    a $ b means a is greater than or equal to b.
    a ↑ b means a is less than b.
    a ● b means a is greater than b.
    a â–² b means a is equal to b.

    Statement:      a ● b, b â–² c, c ₤ d
    Conclusions:   I. d ↑ b
                           II. b â–² d
  4. A.
    if only conclusion (I) follows
    B.
    if only conclusion (II) follows
    C.
    if both conclusions (I) and (II) follows
    D.
    if neither (I) nor (II) follows
    E.
    if either conclusion (I) or (II) follows

  5. p Ûž q means p is neither less than nor equal to q.
    p @ q means p is neither greater than nor equal to q.
    p # q means p is not less than q.
    p ∆ q means p is not greater than q.
    p â–¡ q means p is neither smaller nor greater than q.

    Statement:       p # q, q Ûž r, r ∆ s
    Conclusions:    I. s Ûž p
                            II. q @ s
  6. A.
    if only conclusion (I) follows
    B.
    if only conclusion (II) follows
    C.
    if both conclusions (I) and (II) follows
    D.
    if neither (I) nor (II) follows
    E.
    if either conclusion (I) or (II) follows

  7. P @ Q means P is neither greater than nor equal to Q.
    P # Q means P is not less than Q.
    P $ Q means P is neither greater than nor less than Q.
    P © Q means P is not greater than Q.
    P % Q means P is neither lesser than nor equal to Q.

    Statements:       J % M, J © R, S $ R, S © T.
    Conclusions:       I. J @ S
                               II. T % J
                               III. J $ T
  8. A.
    Only I follows
    B.
    Only II follows
    C.
    Only III follows
    D.
    Either I or II follows
    E.
    None follows

  9. a + b means a is neither less than nor equal to b.
    a - b means a is neither smaller nor greater than b.
    a = b means a is not less than b.
    a * b means a is not greater than b.
    a / b means a is neither greater than nor equal to b.

    Statement:      X + Y, Y * Z, W = Z
    Conclusions:    I. Y * W
                            II. X + Z
  10. A.
    if only conclusion (I) follows
    B.
    if only conclusion (II) follows
    C.
    if both conclusions (I) and (II) follows
    D.
    if neither (I) nor (II) follows
    E.
    if either conclusion (I) or (II) follows

  11. a £ b means a is less than or equal to b.
    a $ b means a is greater than or equal to b.
    a ↑ b means a is less than b.
    a ● b means a is greater than b.
    a â–² b means a is equal to b.

    Statement:      m â–² n, n ₤ o, o ● p
    Conclusion:      I. p ● m
                             II. m ₤ o
  12. A.
    if only conclusion (I) follows
    B.
    if only conclusion (II) follows
    C.
    if both conclusions (I) and (II) follows
    D.
    if neither (I) nor (II) follows
    E.
    if either conclusion (I) or (II) follows

  13. p Ûž q means p is neither less than nor equal to q.
    p @ q means p is neither greater than nor equal to q.
    p # q means p is not less than q.
    p ∆ q means p is not greater than q.
    p â–¡ q means p is neither smaller nor greater than q.

    Statement:               a â–¡ b, c ∆ d, b Ûž c
    Conclusions:            I. a Ûž c
                                     II. b # d
  14. A.
    if only conclusion (I) follows
    B.
    if only conclusion (II) follows
    C.
    if both conclusions (I) and (II) follows
    D.
    if neither (I) nor (II) follows
    E.
    if either conclusion (I) or (II) follows

  15. P @ Q means P is neither greater than nor equal to Q.
    P # Q means P is not less than Q.
    P $ Q means P is neither greater than nor less than Q.
    P © Q means P is not greater than Q.
    P % Q means P is neither lesser than nor equal to Q.

    Statements:           T $ X, X # W, W @ Y, Y % Z.
    Conclusions:          I. T % W
                                   II. X @ Y
                                   III. Z % W
  16. A.
    Only I follows
    B.
    Only II follows
    C.
    Only III follows
    D.
    Either I or II follows
    E.
    None follows

  17. a + b means a is neither less than nor equal to b.
    a - b means a is neither smaller nor greater than b.
    a = b means a is not less than b.
    a * b means a is not greater than b.
    a / b means a is neither greater than nor equal to b.

    Statement:           E / F, F + G, G - H
    Conclusions:        I. E + H
                                II. F + H
  18. A.
    if only conclusion (I) follows
    B.
    if only conclusion (II) follows
    C.
    if both conclusions (I) and (II) follows
    D.
    if neither (I) nor (II) follows
    E.
    if either conclusion (I) or (II) follows

  19. a £ b means a is less than or equal to b.
    a $ b means a is greater than or equal to b.
    a ↑ b means a is less than b.
    a ● b means a is greater than b.
    a â–² b means a is equal to b.

    Statement:           a $ b, b ● c, c ↑ d
    Conclusions:        I. a â–² c
                                 II. b £ d
  20. A.
    if only conclusion (I) follows
    B.
    if only conclusion (II) follows
    C.
    if both conclusions (I) and (II) follows
    D.
    if neither (I) nor (II) follows
    E.
    if either conclusion (I) or (II) follows