Among the following statements, two are contradictory to each other. Select the code that represents them. Statements : (a) All surgeons are doctors. (b) Some surgeons are doctors. (c) Some surgeons are not doctors. (d) No surgeons are doctors. Code
(b) and (d)
To determine which two statements are contradictory, we need to understand what makes two statements contradictory in a logical sense. Two statements are contradictory when one is true and the other must be false.
- Let's analyze each statement:
- Statement (a): "All surgeons are doctors."
- Statement (b): "Some surgeons are doctors."
- Statement (c): "Some surgeons are not doctors."
- Statement (d): "No surgeons are doctors."
In logical terms:
- Statement (a): This implies every surgeon is also a doctor. It leaves no room for any surgeon not being a doctor.
- Statement (b): This implies that there is at least one surgeon who is a doctor, which can coexist with both (a) and (c).
- Statement (c): This implies that there is at least one surgeon who is not a doctor, directly contradicting (a) but not necessarily (b).
- Statement (d): This implies no surgeon is a doctor, directly contradicting (a) and also contradicting (b).
Now, identifying contradictions:
- (a) and (d) are contradictory: If all surgeons are doctors, it cannot be true that no surgeons are doctors.
- (b) and (d) are also contradictory: If some surgeons are doctors, it cannot be true that no surgeons are doctors.
Thus, the contradictory statements are (b) and (d). Hence, the correct option is (b) and (d).
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