Logical Connectivity


Direction: If all the three statements, marked (i), (ii) and (iii) are true, then which one of the following deductions, marked (1), (2), (3) and (4) can be MOST LOGICALLY deduced:

  1. If a student sees a teacher in the class he would not sleep in the class, One day, a student does not see a teacher in the class. Which of the following statements is true?









  1. View Hint View Answer Discuss in Forum

    Here let X be the event that the student sees a teacher. And event Y be the event that he is sleeping. We have been given that X → ~ Y. However, we do not know anything about ~ X, and the question asks us what Y will be if ~ X.
    ∴ We cannot conclude anything.

    Correct Option: C

    Here let X be the event that the student sees a teacher. And event Y be the event that he is sleeping. We have been given that X → ~ Y. However, we do not know anything about ~ X, and the question asks us what Y will be if ~ X.
    ∴ We cannot conclude anything.


  1. In all family photos, if Geeta is present, her two sisters are also present. A certain photo features five members of his family. Among the people in that photo are Geeta's parents with their son. Which of these statements is necessarily true?









  1. View Hint View Answer Discuss in Forum

    Let X be the event that Geeta is present in the photo and event Y that her sister are present. Given that X → Y.
    As per the given information in the photo already has three people (Geeta's parents with their son 3 persons so remaining can be only 2 persons). Thus, Geeta cannot be in the photo.

    Correct Option: B

    Let X be the event that Geeta is present in the photo and event Y that her sister are present. Given that X → Y.
    As per the given information in the photo already has three people (Geeta's parents with their son 3 persons so remaining can be only 2 persons). Thus, Geeta cannot be in the photo.



  1. (i) Doing well in CAT implies doing well in JMET.
    (ii) Good JMET results ensure that you get into one of the IITs or IISc.
    (iii) Poor CAT results do not get you an admission into any of the IIMs.









  1. View Hint View Answer Discuss in Forum

    Admission in one of the IIM's ensures good performance in CAT. This implies doing well in JMET. This ensures that you get into one of the IITS or IISC So option D is true.

    Correct Option: D

    Admission in one of the IIM's ensures good performance in CAT. This implies doing well in JMET. This ensures that you get into one of the IITS or IISC So option D is true.


  1. (i) Whenever there is a fire, the fire alarm goes off
    (ii) If the sprinklers do not start, the fire alarm does not go off.
    (iii) If the sprinklers start, an automatic alarm is set off at the fire department.









  1. View Hint View Answer Discuss in Forum

    Lets eliminate options one by one-
    Option A: Cannot be true since we cannot infer anything if we know that an automatic alarm is set off at the fire department.
    Option B: If sprinklers do not start then the fire alarm doesn't go off. Further we cannot say anything about the automatic alarm at the fire department.
    Option C: When there is a fire the fire alarm goes off so sprinklers start. Hence an automatic alarm is set off at the fire department.
    Option (D) is similarly ruled out.

    Correct Option: C

    Lets eliminate options one by one-
    Option A: Cannot be true since we cannot infer anything if we know that an automatic alarm is set off at the fire department.
    Option B: If sprinklers do not start then the fire alarm doesn't go off. Further we cannot say anything about the automatic alarm at the fire department.
    Option C: When there is a fire the fire alarm goes off so sprinklers start. Hence an automatic alarm is set off at the fire department.
    Option (D) is similarly ruled out.



  1. (i) Whenever milk is kept in front of a child, he/she starts crying.
    (ii) Children cry if they are hungry.
    (iii) Unhappy children are hungry.









  1. View Hint View Answer Discuss in Forum

    Lets eliminate options one by one-
    Option A: Child is hungry, So, from (ii) child is crying, but we cannot say anything about the child liking milk or not.
    Option B: A child is crying, but from this we cannot say anything regarding the child being hungry or unhappy.
    Option C: The statements are not speaking about the happy child.
    Option D: Unhappy children are hungry and hungry children cry. So choice (D) is most logically supported.

    Correct Option: D

    Lets eliminate options one by one-
    Option A: Child is hungry, So, from (ii) child is crying, but we cannot say anything about the child liking milk or not.
    Option B: A child is crying, but from this we cannot say anything regarding the child being hungry or unhappy.
    Option C: The statements are not speaking about the happy child.
    Option D: Unhappy children are hungry and hungry children cry. So choice (D) is most logically supported.