Question

Find the component statements for the following given statements and check whether it is true or false:

(a) A square is a quadrilateral and its four sides are equal

(b) All prime numbers are either even or odd​

Answer 1

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(a) Given statement: A square is a quadrilateral and its four sides are equal

The component statements are:

P: A square is a quadrilateral

Q: A square has all its sides equal.

In this statement, the connecting word is “and”

We know that a square is a quadrilateral

So, the statement P is true.

Also, it is known that all the four sides of a square are equal.

Hence, the statement “Q” is also true.

Therefore, both the component statements are true.

(b) Given statement: All prime numbers are either even or odd

The component statements are:

P: All the prime numbers are odd numbers

Q: All the prime numbers are even numbers

In this statement, the connecting word is “or”

We know that all the prime numbers are not odd numbers

So, the statement P is false.

Also, it is known that all the prime numbers are not even numbers.

Hence, the statement “Q” is also false.

Therefore, both the component statements are not true

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Hope It's Helpful.....:)

Answer 2

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(ᴀ) ɢɪᴠᴇɴ sᴛᴀᴛᴇᴍᴇɴᴛ: ᴀ sϙᴜᴀʀᴇ ɪs ᴀ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ ᴀɴᴅ ɪᴛs ғᴏᴜʀ sɪᴅᴇs ᴀʀᴇ ᴇϙᴜᴀʟ

ᴛʜᴇ ᴄᴏᴍᴘᴏɴᴇɴᴛ sᴛᴀᴛᴇᴍᴇɴᴛs ᴀʀᴇ:

ᴘ: ᴀ sϙᴜᴀʀᴇ ɪs ᴀ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ

ϙ: ᴀ sϙᴜᴀʀᴇ ʜᴀs ᴀʟʟ ɪᴛs sɪᴅᴇs ᴇϙᴜᴀʟ.

ɪɴ ᴛʜɪs sᴛᴀᴛᴇᴍᴇɴᴛ, ᴛʜᴇ ᴄᴏɴɴᴇᴄᴛɪɴɢ ᴡᴏʀᴅ ɪs “ᴀɴᴅ”

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴀ sϙᴜᴀʀᴇ ɪs ᴀ ϙᴜᴀᴅʀɪʟᴀᴛᴇʀᴀʟ

sᴏ, ᴛʜᴇ sᴛᴀᴛᴇᴍᴇɴᴛ ᴘ ɪs ᴛʀᴜᴇ.

ᴀʟsᴏ, ɪᴛ ɪs ᴋɴᴏᴡɴ ᴛʜᴀᴛ ᴀʟʟ ᴛʜᴇ ғᴏᴜʀ sɪᴅᴇs ᴏғ ᴀ sϙᴜᴀʀᴇ ᴀʀᴇ ᴇϙᴜᴀʟ.

ʜᴇɴᴄᴇ, ᴛʜᴇ sᴛᴀᴛᴇᴍᴇɴᴛ “ϙ” ɪs ᴀʟsᴏ ᴛʀᴜᴇ.

ᴛʜᴇʀᴇғᴏʀᴇ, ʙᴏᴛʜ ᴛʜᴇ ᴄᴏᴍᴘᴏɴᴇɴᴛ sᴛᴀᴛᴇᴍᴇɴᴛs ᴀʀᴇ ᴛʀᴜᴇ.

(ʙ) ɢɪᴠᴇɴ sᴛᴀᴛᴇᴍᴇɴᴛ: ᴀʟʟ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀs ᴀʀᴇ ᴇɪᴛʜᴇʀ ᴇᴠᴇɴ ᴏʀ ᴏᴅᴅ

ᴛʜᴇ ᴄᴏᴍᴘᴏɴᴇɴᴛ sᴛᴀᴛᴇᴍᴇɴᴛs ᴀʀᴇ:

ᴘ: ᴀʟʟ ᴛʜᴇ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀs ᴀʀᴇ ᴏᴅᴅ ɴᴜᴍʙᴇʀs

ϙ: ᴀʟʟ ᴛʜᴇ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀs ᴀʀᴇ ᴇᴠᴇɴ ɴᴜᴍʙᴇʀs

ɪɴ ᴛʜɪs sᴛᴀᴛᴇᴍᴇɴᴛ, ᴛʜᴇ ᴄᴏɴɴᴇᴄᴛɪɴɢ ᴡᴏʀᴅ ɪs “ᴏʀ”

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴀʟʟ ᴛʜᴇ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀs ᴀʀᴇ ɴᴏᴛ ᴏᴅᴅ ɴᴜᴍʙᴇʀs

sᴏ, ᴛʜᴇ sᴛᴀᴛᴇᴍᴇɴᴛ ᴘ ɪs ғᴀʟsᴇ.

ᴀʟsᴏ, ɪᴛ ɪs ᴋɴᴏᴡɴ ᴛʜᴀᴛ ᴀʟʟ ᴛʜᴇ ᴘʀɪᴍᴇ ɴᴜᴍʙᴇʀs ᴀʀᴇ ɴᴏᴛ ᴇᴠᴇɴ ɴᴜᴍʙᴇʀs.

ʜᴇɴᴄᴇ, ᴛʜᴇ sᴛᴀᴛᴇᴍᴇɴᴛ “ϙ” ɪs ᴀʟsᴏ ғᴀʟsᴇ.

ᴛʜᴇʀᴇғᴏʀᴇ, ʙᴏᴛʜ ᴛʜᴇ ᴄᴏᴍᴘᴏɴᴇɴᴛ sᴛᴀᴛᴇᴍᴇɴᴛs ᴀʀᴇ ɴᴏᴛ ᴛʀᴜᴇ

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ʜᴏᴘᴇ ɪᴛ's ʜᴇʟᴘғᴜʟ.....:)