Identifying the Contradictory of an A Proposition
In traditional logic, propositions are related in a structure known as the Square of Opposition. The contradictory relationship means that two propositions cannot both be true and cannot both be false; one must be true, and the other must be false.
Contradictory Relationship Explained
- A Proposition: This is a Universal Affirmative statement (e.g., "All humans are mortal").
- Contradictory Pairs: In the Square of Opposition, the pairs of contradictory propositions are:
- A and O
- E and I
- A and O: The 'A' proposition (Universal Affirmative) and the 'O' proposition (Particular Negative, e.g., "Some humans are not mortal") are contradictories. If "All humans are mortal" is true, then "Some humans are not mortal" must be false. If "All humans are mortal" is false, then "Some humans are not mortal" must be true.
Conclusion
Therefore, the contradictory of an 'A' proposition is the 'O' proposition.
Important Questions from Syllogism
- Consider the following sentences:
All benches are beds .No bed is a bulb. Some bulbs are lamps.
Which of the following can be inferred?
i. Some beds are lamps.
ii. Some lamps are beds. Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.
Statements:
I. No manager is a leader.
II. All leaders are executives.
Conclusions:
I. No manager is an executive.
II. No executive is a manager.Given below are two statements 1 and 2, and two conclusions I and II.
Statement 1: All entrepreneurs are wealthy.
Statement 2: All wealthy are risk seekers.
Conclusion I: All risk seekers are wealthy.
Conclusion II: Only some entrepreneurs are risk seekers.
Based on the above statements and conclusions, which one of the following options is CORRECT?
Statements:
1. All heroes are winners.
2. All winners are lucky people.
Inferences:
I. All lucky people are heroes.
II. Some lucky people are heroes.
III. Some winners are heroes.
Which of the above inferences can be logically deduced from statements 1 and 2?Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty?
(i) All human beings are cruel creatures.
(ii) Some human beings are cruel creatures.
(iii) Some creatures that are cruel are human beings.
(iv) No human beings are cruel creatures.
