Question

1) Translate the following statement into symbolic form.
i) Rahul passed in Hindi and English.

2) Translate the following statement into symbolic form.
ii) $x$ and $y$ are even integers.

3) Translate the following statement into symbolic form.
iii) $2,3$ and $6$ are factors of $12$

4) Translate the following statement into symbolic form.
iv) Either $x\text{or}x+1$ is an odd integer.

5) Translate the following statement into symbolic form.
v) A number is either divisible by $2\text{or}3$

6) Translate the following statement into symbolic form.
vi) Either $x=2\text{or}x=3$ is a root of $3x^2-x-10=0$

7) Translate the following statement into symbolic form.
vii) Students can take Hindi or English as an optional paper.

Answer 1

1) Given statement: ''Rahul passed in Hindi and English''

Component statements:

$p$: Rahul passed in Hindi

$q$ : Rahul passed in English

$\therefore$ The symbolic form of given statement is $p\Lambda q$

2) Given statement: ${}^{\prime \prime }x\text{and}y\text{are even integers''.}$

Component statements:

$p:x$ is even integer.

$q:y$ is an even integer.

$\therefore$ The symbolic form of given statement is

$p\Lambda q.$

3) Given statement : ${}^{\prime \prime }2,3\text{and}6\text{are factors of}{12}^{\prime \prime }.$

Component statements:

$p:2$ is a factor of $12.$

$q:3$ is a factor of $12.$

$r:6$ is a factor of $12.$

$\therefore$ The symbolic form of given statement is

$p\Lambda q\Lambda r.$

4) given statement : ''Either $xorx+1$ is an odd integer.''

Component statements :

$p:x$ is an odd integer

$q:x+1$ is an odd integer

$\therefore$ The symbolic form of given statement is

$p\vee q.$

5) Given statement : '' A number is either divisible by 2 or 3''.

Component statements:

$p:A$ number is divisible by $2$

$q:A$ number is divisible by $3$

$\therefore$ The symbolic form of given statement is

$p\vee q.$

6) Given statement: '' Either $x=2orx=3\text{is a root of}3x^2-x-10=0^{\prime \prime }$

Component statements:

$p:x=2\text{is a root of}3x^2-x-10=0$

$q:x=3\text{is a root of}3x^2-x-10=0$

$\therefore$ The symbolic form of given statement is

$p\vee q.$

7) Given statement: ''Students can take Hindi or English as an optional paper.''

Component statements:

$p:$ Students can take Hindi as an optional paper

$q:$ Students can take English as an optional paper

$\therefore$ The symbolic form of given statement is

$p\vee q.$