(I): A valid deductive argument that also has all true premises is called a sound argument
(II): A strong inductive argument that has all true premises is called a cogent argument
In the light of the above statements, choose the most appropriate answer from the options given below
Understanding Sound Deductive Arguments
Statement (I) defines a sound argument. In logic, a deductive argument aims to provide premises that guarantee the truth of the conclusion. Such an argument is called valid if it's structured such that if all the premises were true, the conclusion would have to be true.
However, validity only concerns the structure. For a deductive argument to be sound, it must meet two conditions:
- The argument must be valid (the conclusion logically follows from the premises).
- All of the argument's premises must be true in reality.
Therefore, the statement 'A valid deductive argument that also has all true premises is called a sound argument' is a correct definition.
Understanding Cogent Inductive Arguments
Statement (II) defines a cogent argument. An inductive argument, unlike a deductive one, aims to provide premises that make the conclusion likely or probable, but not guarantee it. Such an argument is called strong if its premises provide good evidence for the conclusion, making it probable.
For an inductive argument to be considered cogent, it must meet these conditions:
- The argument must be strong (the premises make the conclusion probable).
- All of the argument's premises must be true.
Thus, the statement 'A strong inductive argument that has all true premises is called a cogent argument' is also a correct definition.
Conclusion on Argument Validity
Based on the analysis of both statements:
- Statement (I) accurately defines a sound deductive argument.
- Statement (II) accurately defines a cogent inductive argument.
Since both statements provide correct definitions for their respective types of arguments, the most appropriate choice is that both I and II are correct.
Important Questions from Assertion and Reasons (Notes)
- Given below are two statements one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A A sample survey is usually extensive in scope
Reason R Therfore, both in the number of cases included and in the manner of their selection, it has to be adequately and faithfully representative of a larger population. - Select the option that is true regarding the following two statements labelled Assertion (A) and Reason (R).
Assertion (A): A rubber band is a solid because it regains its original shape when the stretching force is removed.
Reason (R): Solids are rigid and have negligible compressibility. - Two statements are given below. One is Assertion (A) and the other is Reason (R). Choose the correct answer from the options given for these statements.
Assertion (A): Properties of a compound are different from those of its constituent elements.
Reason (R): Compounds are formed by chemical combination of elements in a fixed ratio. - Which of the following statements are correct?
(i) Solid $CO_2$ is called dry ice.
(ii) Solid $CO_2$ changes directly into gas at 1 atm pressure.
(iii) Pressure and temperature can change the state of matter.
(iv) Solid $CO_2$ melts into liquid $CO_2$ before becoming gas. - Select the option that is true regarding the following two statements labelled Assertion (A) and Reason (R).
Assertion (A): Copper wire in iron sulphate solution shows no visible reaction.
Reason (R): Copper is less reactive than iron.
