The statement pqpis equivalent to
Find the component statements of the following compound statements and check whether they are true or false.(i) Number 3 is prime or it is odd.(ii) All integers are positive or negative.(iii) 100 is divisible by 3, 11 and 5.
Find out whether the following sentences is a statement or not. Justify your answer: the real number x is less than 2.
Rewrite the following statement in the form p if only ifq: If a tumbler is half empty, then it is half full and if a tumbler is half full, then it is half empty.
Are the following pairs of statements negations of each other:(i) The number x is not a rational number. The number x is not an irrational number.(ii) The number x is a rational number. The number x is an irrational number.
Rewrite each of the following statements in the form “p if and only if q(i) p: If you watch television, then your mind is free and if your mind is free, then you watch television.(ii) q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.(iii) r : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.
Determine the contrapositive of each of the following statements: (i)If Mohan is a poet, then he is poor. (ii)If she works, she will earn money. (iii)It never rains when it is cold.