Question

The negation of the statement, “I go to school every day”, is
(a) I never go to school.
(b) Some days, I do not go to school.
(c) Not all the days I do not go to school.
(d) All day I go to school.

Answer 1

Hint: Focus on the point that negation of a statement is a statement which can never be true simultaneously with the parent statement and the parent statement and its negative are mutually exclusive, i.e., one of the statements out of the two will be always true.

Complete step-by-step solution -
Before moving to the options, let us discuss the meaning of different symbols used in the Boolean expression. See the symbols that we see in the Boolean expressions are called logic symbols, and this includes:
$\wedge$ - represents the AND logical operation.
$\vee$ - represents the OR logical operation.
$\sim$ - represents the NOT logical operator.
$\to$ - represents the if-then logical operator.
The statement given to us is “I go to school every day.”
Among the given options, option (d) all days I go to school., means the same as the original statement so it cannot be its negation. Also option (a) means that he never goes to school while the original statement means he goes to school every day, but leaving this case there are still many cases like he goes to school 2 days a week etc. so option (a) is also not an answer.
Now if you see option (c), it puts a constraint that student will not miss the class every day, so the two statements, i.e., the original one and option (c) are not exclusive, as both of them don’t cover the case that the student misses the school every day.
Therefore, the answer is option (b), as it says some days I don’t go to school, which means he misses at least one day of school which is covered by the original statement.
Hence, the answer is option (b).

Note: Be very careful, as in such questions the play of words is very complicated. Immediately after reading the question, you will think the answer is option (a) “I never go to school”, but option (a) is the negative form of the given statement not the negation. Always remember, two statements are negation of each other if they are mutually exclusive and have no overlapping cases.