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For each of the following statement dete...

For each of the following statement determine which type of 'or ' is used ? Also check whether the compound statement is true or false.
(i) 5 is prime or odd.
(ii) school is closed if there is a holiday or Sunday.
(iii) a tie or a T-shirt is free on puchasing a coat.

Text Solution

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(i) component statements are :
p: 5 is prime.
q : 5 is odd. Here 5 is prime as well as odd, so inclusive 'or' is used.
`because` p and q both are true.
`because` the compound statement is true.
(ii) component statements are :
p: school is closed if there is a holiday. q , school is closed if there is sunday. here school is closed on a holiday as well as on sunday, so inclusive 'or' is used.
(iii) component statements are :
p: a tie is free on purchasing a coat. q: a T-shirt is free on purchasing a coat. here on purchasing a coat, either a tie or a T-shirt is free, both are not free simultaneously, so excelusive 'or' is used.
`because` p and q both are true.
`because` the compound statements is true.
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