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Question

Split each of the following into simple sentences and determine whether it is true or false. Also, determine whether an 'inclusive or' or 'exclusive or' is used. (i) The sum of 3 and 7 is 10 or 11. (ii) (1+i) is a real or a complex number. (iii) Every quadratic equation has one or two real roots. (iv) You are wet when it rains or you are in a river. (v) 24 is a multiple of 5 or 8. (vi) Every integer is rational or irrational. (vii) For getting a driving licence you should have a ration card or a passport. (viii) 100 is a multiple of 6 or 8. (ix) Square of an integer is positive or negative. (x) Sun rises or Moon sets.

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Solution

(i) p: The sum of 3 and 7 is 10. q: The sum of 3 and 7 is 11. (p or q) is true. 'or is exclusive' (ii) p: (1+i) is a real number. q: (1+i) is a complex number. (p or q) is true. 'or is exclusive' (iii) p: Every quadratic equation has one real root. q: Every quadratic equation has two real roots. (p or q) is false. (iv) p: You are wet when it rains. q: You are wet when you are in a river. (p or q) is true. 'or is inclusive' (v) Let p: 24 is a multiple of 5. and q: 24 is a multiple of 8. (p or q) is true. 'or is exclusive' (vi) Let p: Every integer is rational. q: Every integer is irrational. (p or q) is true. 'or is exclusive' (vii) Let p: For getting a driving licence you should have a ration card. q: For getting a driving licence you should have a passport. (p or q) is true. 'or is inclusive' (viii) Let p: 100 is a multiple of 6. q: 100 is a multiple of 8. (p or q) is false. (ix) Let p: Square of an integer is positive. q: Square of an integer is negative. (p or q) is false. [02 is not positive.] (x) Let p: Sun rises. q: Moon sets. (p or q) is true. 'or is exclusive'

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