Question

HOLA BRAINLY MATES In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

Answer 1

60 .

$\huge\bold{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

• In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French .

TO FIND :-

• How many speak at least one of these two languages ?

CALCULATION :-

Let, M be the set of people in the committee who speak French .

And N be the set of people in the committee who speak Spanish .

✍️ Now,

Number of people who speak French = n(M)

• => n(M) = 50 .

And Number of people who speak Spanish = n(N)

• => n(N) = 20 .

✍️ Number of people who speak both French and Spanish = $\rm{n\:(M\:\cap\:N)\:}$

• $\rm{\implies\:n\:(M\:\cap\:N)\:=\:10\:}$

✍️ Number of people who speak at least one of these two languages = $\rm{\purple{n\:(M\:\cup\:N)\:}}$

✍️ We have know that,

$\red\bigstar\:\rm{\green{\boxed{\orange{n\:(M\:\cup\:N)\:=\:n\:(M)\:+\:n\:(N)\:-\:n\:(M\:\cap\:N)\:}}}}$

$\rm{\implies\:n\:(M\:\cup\:N)\:=\:50\:+\:20\:-\:10\:}$

$\rm{\implies\:n\:(M\:\cup\:N)\:=\:70\:-\:10\:}$

$\rm{\pink{\implies\:n\:(M\:\cup\:N)\:=\:60\:}}$

$\therefore$ $<font color=baby>$ There are 60 people in the committee who speak at the one of these two languages .

Answer 2

$\boxed{ \displaystyle\rm\green{Answer\:}}$

Lᴇᴛ F ʙᴇ ᴛʜᴇ sᴇᴛ ᴏғ ᴘᴇᴏᴘʟᴇ ɪɴ ᴛʜᴇ ᴄᴏᴍᴍɪᴛᴛᴇᴇ ᴡʜᴏ sᴘᴇᴀᴋ Fʀᴇɴᴄʜ, ᴀɴᴅ

S ʙᴇ ᴛʜᴇ sᴇᴛ ᴏғ ᴘᴇᴏᴘʟᴇ ɪɴ ᴛʜᴇ ᴄᴏᴍᴍɪᴛᴛᴇᴇ ᴡʜᴏ sᴘᴇᴀᴋ Sᴘᴀɴɪsʜ

∴ ɴ(F) = 50, ɴ(S) = 20, ɴ(S ∩ F) = 10

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ:

ɴ(S ∪ F) = ɴ(S) + ɴ(F) – ɴ(S ∩ F)

= 20 + 50 – 10

= 70 – 10 = 60

Tʜᴜs, 60 ᴘᴇᴏᴘʟᴇ ɪɴ ᴛʜᴇ ᴄᴏᴍᴍɪᴛᴛᴇᴇ sᴘᴇᴀᴋ ᴀᴛ ʟᴇᴀsᴛ ᴏɴᴇ ᴏғ ᴛʜᴇ ᴛᴡᴏ ʟᴀɴɢᴜᴀɢᴇs.

Step-by-step explanation:

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