Implication or conditional in Mathematical Logic.<br />Hello friends, Welcome to my channel mathstips4u.<br />In this channel I uploaded videos on Mathematics for the students of 11th and 12th class. In these video I have given tips and tricks that helps the students to overcome fear of facing board exam.<br />In my last video we have seen negation and its truth table.<br />In this video we are going to learn implication (or conditional) and its truth tables and some of its examples.<br />So we shall begin with <br />Implication or conditional [→]:<br />Let p and q be two simple statements. Then the compound statement ‘If p then q’ is called the conditional or implication, and denoted by p → q or p =＞ q. It is read as p implies q.<br />In the implication p → q, p is called antecedent or hypothesis and q is called the consequent or conclusion.<br />p → q is defined to have the truth value ‘false’ if p has truth value ‘true’ and q has truth value ‘false’. In all other cases, p → q is defined to have the truth value ‘true’.<br />Truth table of implication p → q<br />p q p → q<br />T T T<br />T F F<br />F T T<br />F F T<br />Remember: p → q and q → p both are not the same.<br />Following are phrases in English which are equivalent to (p → q)<br />1.p is sufficient for q.<br />2. q is necessary for p.<br />3. p only if q. <br />4. q follows p.<br />5.q provided p.<br />6. q if p.<br />Ex. Express following in symbolic form.<br />1. Visiting Himalayas implies peace of mind.<br />2. I shall come provided I finish my work.<br />3. A family becomes literate if the women in it are literate.<br />4. Rights follow from performing the duties sincerely.<br />5. x = 1 only if x^2 = x.<br />6. The sufficient condition for being rich is to be rational.<br />7. Getting bonus is necessary condition for me to purchase a car.<br />Solution:<br />1. Visiting Himalayas implies peace of mind.<br />First we write the given statement by using if …then.<br />‘If I visit Himalayas, then I will get peace of mind’ <br /> p: I visit Himalayas.<br />q: I get peace of mind.<br />The symbolic form is p → q.<br /> The remaining are left intentionally as exercise for you. Try it or wait till my next video on bi-conditional is uploaded in my channel “mathstips4u”.<br />In this way we have seen implication and its truth tables and some of its examples.<br />In my next video we are going to learn Bi-conditional or double implication and its truth table.<br />If you like my video, please subscribe my channel, like it, share it and comment it.<br /> Thanking you for watching my video.<br />
