Correct Option (2)
Based on the provided statements:
- Statement 1, as interpreted by the solution, indicates the family comprises a man, his wife, two sons, and two daughters.
- Statement 2 specifies that the two daughters were invited to a feast, and the male members of the family (the man and his two sons) went out for a picnic.
- Statement 3, regarding the man's father not returning from work, implies he is not at home.
From these deductions, the wife is the only explicitly mentioned family member who remains at home. Therefore, it is certain that the man's wife was left at home. The option "It is likely that the man’s wife was left at home" is considered correct because while her presence is a direct deduction, the term "likely" accommodates the possibility of other unmentioned individuals being present, as the statements do not explicitly define the entire household or definitively state that only the wife remained.
Incorrect Options:
Option 1: Only the man’s wife was left at home.
While the wife was left at home, the statements do not explicitly confirm that she was the sole person remaining. The information provided defines specific family members and their movements, but does not definitively preclude the existence of other unmentioned individuals within the household.
Option 3: None was left at home.
This statement is incorrect. As deduced from the given information, the man's wife remained at home after the daughters went to a feast and the male members went for a picnic.
Option 4: More than one person was left at home.
There is no information provided in the statements to support the conclusion that more than one person was left at home. Only the wife's presence at home is directly deducible from the given facts.