Write the following statements in symbolic form:i. Ramesh is cruel or

1.	Write the following statements in symbolic form:i. Ramesh is cruel or strict.ii. I am brave is necessary and sufficient condition to climb the Mount Everest.iii. I can travel by train provided I get my ticket reserved.iv. Sandeep neither likes tea nor coffee but enjoys a soft-drink.v. ABC is a triangle only if AB + BC > AC.vi. Rajesh is studious but does not get good marks.
Answer» i. Let p: Ramesh is cruel, q: Ramesh is strict. \(\therefore\)The symbolic form of the given statement is p \(\lor\) q. ii. Let p: I am brave. q: I can climb the Mount Everest. \(\therefore\) The symbolic form of the given statement is p \(\leftrightarrow\) q. iii. Let p: I can travel by train, q: I get my ticket reserved. \(\therefore\)The symbolic form of the given statement is q \(\leftrightarrow\) p. iv. Let p: Sandeep likes tea, q: Sandeep likes coffee. r: Sandeep enjoys a soft-drink. \(\therefore\) The symbolic form of the given statement is (~p \(\land\) ~q) \(\land\) r. v. Let p: ABC is a triangle, q: AB + BC > AC. \(\therefore\) The symbolic form of the given statement is p \(\rightarrow\) q. vi. Let p: Rajesh is studious, q: Rajesh gets good marks. \(\therefore\) The symbolic form of the given statement is p \(\land\) ~q.

Write the following statements in symbolic form:i. Ramesh is cruel or strict.ii. I am brave is necessary and sufficient condition to climb the Mount Everest.iii. I can travel by train provided I get my ticket reserved.iv. Sandeep neither likes tea nor coffee but enjoys a soft-drink.v. ABC is a triangle only if AB + BC > AC.vi. Rajesh is studious but does not get good marks.

Answer»

i. Let p: Ramesh is cruel,

q: Ramesh is strict.

\(\therefore\)The symbolic form of the given statement is p \(\lor\) q.

ii. Let p: I am brave.

q: I can climb the Mount Everest.

\(\therefore\) The symbolic form of the given statement is p \(\leftrightarrow\) q.

iii. Let p: I can travel by train,

q: I get my ticket reserved.

\(\therefore\)The symbolic form of the given statement is q \(\leftrightarrow\) p.

iv. Let p: Sandeep likes tea,

q: Sandeep likes coffee.

r: Sandeep enjoys a soft-drink.

\(\therefore\) The symbolic form of the given statement is

(~p \(\land\) ~q) \(\land\) r.

v. Let p: ABC is a triangle,

q: AB + BC > AC.

\(\therefore\) The symbolic form of the given statement is p \(\rightarrow\) q.

vi. Let p: Rajesh is studious,

q: Rajesh gets good marks.

\(\therefore\) The symbolic form of the given statement is p \(\land\) ~q.