or a Sunday. (iii) Two lines intersect at a point or are parallel . (iv) Students can take French or Sanskrit as their third language. Solution (i)Here “Or” is inclusive since a person can have both a passport and a voter registration card to enter a country.
Here also “Or” is inclusive since school is closed on holiday as well as on Sunday. (iii) Here “Or” is exclusive because it is not possible for two lines to intersect and parallel together. (iv) Here also “Or” is exclusive because a student cannot take both French and Sanskrit. Rule for the compound statement with ‘Or’ .
A compound statement with an ‘Or’ is true when one component statement is true or both the component statements are true. . A compound statement with an ‘Or’ is false when both the component statements are false. For example, consider the following statement.
p: Two lines intersect at a point or they are parallel The component statements are q : Two lines intersect at a point. r : Two lines are parallel. Then, when q is true r is false and when r is true q is false. Therefore, the compound statement p is true.
Consider another statement. p : is a multiple of or . Its component statements are q : is a multiple of . r : is a multiple of .
Both q and r are false. Therefore, the compound statement p is false. MATHEMATICAL REASONING Again, consider the following statement: p: The school is closed, if there is a holiday or Sunday. The component statements are q : School is closed if there is a holiday.
r : School is closed if there is a Sunday. Both q and r are true, therefore, the compound statement is true. Consider another statement. p : Mumbai is the capital of Kolkata or Karnataka.
The component statements are q : Mumbai is the capital of Kolkata. r : Mumbai is the capital of Karnataka. Both these statements are false. Therefore, the compound statement is false.
Let us consider some