Consider the following statement : “We shall go either for a picnic or for trekking”. Which of the following, if true, would falsify this claim ?

(a) We go for a picnic but not for trekking
(b) Activities such as picnic and trekking are encouraged by the health authorities
(c) We go for trekking and not for picnic
(d) We do not go either for picnic or for trekking ✓ UPSC's answer

Why the answer is (d)

• The statement 'We shall go either for a picnic or for trekking' is a logical disjunction (A or B), which is true if at least one of the activities occurs.

• To falsify a disjunction, both components must be false; that is, neither activity can take place.

• Option (a) describes going for a picnic, which satisfies the 'or' condition, making the statement true.

• Option (c) describes going for trekking, which also satisfies the 'or' condition, making the statement true.

• Option (d) states that we do not go for either activity, meaning both 'picnic' and 'trekking' are false.

• Since neither activity occurs, the original claim that at least one would happen is proven false.

Why the other options are wrong

(a) We go for a picnic but not for trekking: Going for a picnic satisfies the condition of going for 'either a picnic or trekking', so the statement remains true.
(b) Activities such as picnic and trekking are encouraged by the health authorities: The encouragement of activities by health authorities is irrelevant to the factual outcome of whether the group actually goes for either activity.
(c) We go for trekking and not for picnic: Going for trekking satisfies the condition of going for 'either a picnic or trekking', so the statement remains true.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2016, held on 7 August 2016. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.