For the given statements identify the necessary and sufficient conditions. t: If you drive over 80 km per hour, then you will get a fine.

The contrapositives of few conditional statements are given below , find the conditional statements : If you do not have winter clothes , then you do not live in simla .

Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (a) If you live in Delhi, then you have winter clothes. (i) If you do not have winter clothes, then you do not live in Delhi. (ii) If you have winter clothes, then you live in Delhi.

Two pairs of statements p and q are given below . Combine theses two statements using the biconditional phrase "if and only if " . p : If your mind is free , then you watch T .V . q : If you watch T . V then your mind is free .

Rewrite each of the following statements in the form ''p if and only if q'' q: For you to get an A grade, it is necessary and sufficient that you do all the homework regularly.

Write each of the following statements in the form ''if-then'' To get an A^(+) in the class, it is necessary that you do all the exercises of the book.

A uniform magnetic field of 100 G (IG=10^(-4)T) exists in a region of length about 10 cm and area of cross- section about 10^(-3)m^(2) . The maximum current carrying capacity of a given coil of wire is 15A and the number of turns per unit length that can be wound round a core is at most 1000 turns m^(-1) . How would you utils the coil to design a solenoid for the required purpose ? Assume the core is not ferromagnetic.