Write the component statements of the following compound statements and check whether the compound statement is true or false :
(i) To enter into a public library children need an identity card from the school or a letter from the school authorities.
(ii) All rational numbers are real and all real numbers are not complex.
(iii) Square of an integer is positive or negative.
(iv) x = 2 and x = 3 are the roots of the equation 3x2−x−10=0.
(v) The sand heats up quickly in the sun and does not cool down fast at night.
Write the component statements of the following compound statements and check whether the compound statement is true or false :
(i) To enter into a public library children need an identity card from the school or a letter from the school authorities.
(ii) All rational numbers are real and all real numbers are not complex.
(iii) Square of an integer is positive or negative.
(iv) x = 2 and x = 3 are the roots of the equation 3x2−x−10=0.
(v) The sand heats up quickly in the sun and does not cool down fast at night.
The component statement of the compound statement
To enter into a public library children need an identity card from the school or a letter from the school authorities.
are
p : To get into a public library children need an identity card.
q : To get into a public library children need a letter from the school authorities.
We know that if p and q are true then p or q must also be true.
Hence, the compound ststement is true.
(ii) The component statement of the compound statement.
All rational numbers are real and all real numbers are not complex.
are
p : All rational numbers are real
q : All real numbers are not complex.
We know that p is true and q is false.
∴ The compound statement " p and q " is false .
(iii) The compound statement of the compound statement
Square of an integer is positive or negative.
are
p : Square of an integer is positive
q : Square of an integer is negative.
We know that if p and q are true then p or q must also be true.
Hence, the compound statement is true.
(iv) The compound statement of the compound statement
x = 2 and x = 3 are the roots of the equation 3x2−x−10=0.
are
p : x = 2 is a roots of the equation 3x2−x−10=0.
q : x = 3 is a roots of the equation 3x2−x−10=0.
Here, p is true but q is false.
∴ The compound statement " p and q " is false.
(v) The component statement of the compound statement
The sand heats up quickly in the sun and does not cool down fast at night are
p : The sand heats up quickly in the sun
q : The sand does not cool down fast at night.
The compound statement p and q is false, because p is true and q is false.
The component statement of the compound statement
To enter into a public library children need an identity card from the school or a letter from the school authorities.
are
p : To get into a public library children need an identity card.
q : To get into a public library children need a letter from the school authorities.
We know that if p and q are true then p or q must also be true.
Hence, the compound ststement is true.
(ii) The component statement of the compound statement.
All rational numbers are real and all real numbers are not complex.
are
p : All rational numbers are real
q : All real numbers are not complex.
We know that p is true and q is false.
∴ The compound statement " p and q " is false .
(iii) The compound statement of the compound statement
Square of an integer is positive or negative.
are
p : Square of an integer is positive
q : Square of an integer is negative.
We know that if p and q are true then p or q must also be true.
Hence, the compound statement is true.
(iv) The compound statement of the compound statement
x = 2 and x = 3 are the roots of the equation 3x2−x−10=0.
are
p : x = 2 is a roots of the equation 3x2−x−10=0.
q : x = 3 is a roots of the equation 3x2−x−10=0.
Here, p is true but q is false.
∴ The compound statement " p and q " is false.
(v) The component statement of the compound statement
The sand heats up quickly in the sun and does not cool down fast at night are
p : The sand heats up quickly in the sun
q : The sand does not cool down fast at night.
The compound statement p and q is false, because p is true and q is false.
