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Translate the following statements into symbolic form :
(i) Rahul passed in Hindi and English.
(ii) $\mathrm{x}$ and $\mathrm{y}$ are even integers.
(iii) 2,3 and 6 are factors of 12 .
(iv) Either $x$ or $x+1$ is an odd integer.
(v) A number is either divisible by 2 or 3 .
(vi) Either $\mathrm{x}=2$ or $\mathrm{x}=3$ is a root of $3 \mathrm{x}^2-\mathrm{x}-10=0$.
(vii) Students can take Hindi or English as an optional paper.
(i) Rahul passed in Hindi and English.
(ii) $\mathrm{x}$ and $\mathrm{y}$ are even integers.
(iii) 2,3 and 6 are factors of 12 .
(iv) Either $x$ or $x+1$ is an odd integer.
(v) A number is either divisible by 2 or 3 .
(vi) Either $\mathrm{x}=2$ or $\mathrm{x}=3$ is a root of $3 \mathrm{x}^2-\mathrm{x}-10=0$.
(vii) Students can take Hindi or English as an optional paper.
Solution:
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Verified Answer
(i) $P \wedge q$, where $p:$ Rahul passed in Hindi; $q$ : Rahul passed in English.
(ii) $\mathrm{p} \wedge \mathrm{q}$, where $\mathrm{p}: \mathrm{x}$ is an even integer ; $q: y$ is an even integer.
(iii) $\mathrm{p} \wedge \mathrm{q}, \wedge \mathrm{r}$ where $\mathrm{p}: 2$ is factor of 12 ; $q: 3$ is factor of $12 ; r: 6$ is factor of 12 .
(iv) $\mathrm{p} \vee \mathrm{q}$, where $\mathrm{p}: \mathrm{x}$ is an odd integer ; $\mathrm{q}: \mathrm{x}+1$ is an odd integer.
(v) $\mathrm{p} \vee \mathrm{q}$, where $\mathrm{p}$ : a number is divisible by $2, \mathrm{q}: \mathrm{a}$ number is divisible by 3 .
(vi) $\mathrm{p} \vee \mathrm{q}$, where $\mathrm{p} ; \mathrm{x}=2$ is a root of $3 \mathrm{x}^2-\mathrm{x}-10=0, \mathrm{q}: \mathrm{x}=3$ is a root of $3 x^2-x-10=0$.
(vii) $\mathrm{p} \vee \mathrm{q}$, where $\mathrm{p}$ : student can take Hindi as an optional paper.
q : student can take English as an optional paper.
(ii) $\mathrm{p} \wedge \mathrm{q}$, where $\mathrm{p}: \mathrm{x}$ is an even integer ; $q: y$ is an even integer.
(iii) $\mathrm{p} \wedge \mathrm{q}, \wedge \mathrm{r}$ where $\mathrm{p}: 2$ is factor of 12 ; $q: 3$ is factor of $12 ; r: 6$ is factor of 12 .
(iv) $\mathrm{p} \vee \mathrm{q}$, where $\mathrm{p}: \mathrm{x}$ is an odd integer ; $\mathrm{q}: \mathrm{x}+1$ is an odd integer.
(v) $\mathrm{p} \vee \mathrm{q}$, where $\mathrm{p}$ : a number is divisible by $2, \mathrm{q}: \mathrm{a}$ number is divisible by 3 .
(vi) $\mathrm{p} \vee \mathrm{q}$, where $\mathrm{p} ; \mathrm{x}=2$ is a root of $3 \mathrm{x}^2-\mathrm{x}-10=0, \mathrm{q}: \mathrm{x}=3$ is a root of $3 x^2-x-10=0$.
(vii) $\mathrm{p} \vee \mathrm{q}$, where $\mathrm{p}$ : student can take Hindi as an optional paper.
q : student can take English as an optional paper.
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