Check the validity of the following statements :
(i) p : 100 is a multiple of 4 and 5.
(ii) q : 125 is a multiple of 5 and 7.
(iii) r : 60 is a multiple of 3 or 5.
Check the validity of the following statements :
(i) p : 100 is a multiple of 4 and 5.
(ii) q : 125 is a multiple of 5 and 7.
(iii) r : 60 is a multiple of 3 or 5.
(i) The statement is :
"100 is a multiple of 4 and 5."
We know that 100 is a multiple of 4 as well as 5. So, p is true statement.
Hence, the statement is true i.e. the statement "p"
is a valid statement.
(ii) The statement is :
"125 is a multiple of 5 and 7"
Since 125 is a multiple of 5 but it is not a multiple of 7. So, q is not a true statement i.e. the statement "q" is not a valid statement.
(iii) The statement is :
r : 60 is a multiple of 3 or 5
is a compound statement of the following statements :
p : 60 is multiple of 3
q : 60 is multiple of 5
Suppose q is false. That is, 60 is not a multiple of 5. Clearly p is true.
Thus, if we assume that q is false, then p is true.
Hence, the statement is true i.e. the statement "r" is a valid statement.
(i) The statement is :
"100 is a multiple of 4 and 5."
We know that 100 is a multiple of 4 as well as 5. So, p is true statement.
Hence, the statement is true i.e. the statement "p"
is a valid statement.
(ii) The statement is :
"125 is a multiple of 5 and 7"
Since 125 is a multiple of 5 but it is not a multiple of 7. So, q is not a true statement i.e. the statement "q" is not a valid statement.
(iii) The statement is :
r : 60 is a multiple of 3 or 5
is a compound statement of the following statements :
p : 60 is multiple of 3
q : 60 is multiple of 5
Suppose q is false. That is, 60 is not a multiple of 5. Clearly p is true.
Thus, if we assume that q is false, then p is true.
Hence, the statement is true i.e. the statement "r" is a valid statement.
