Given that the product of two rational numbers is rational, and suppose a and b are rationals, what can you conclude about ab ?

Given that sqrtp is irrational for all primes p,and suppose that 19423 is a prime. What can you conclude about sqrt 19423 ?

Given that y =-6x + 5 and suppose x= 3. What is y?

Given that y = x^2 +6 and x = -1 , what can we conclude about the value of y ?

Given that the decimal expansion of irrational numbers is non-terminating, non-recurring, and sqrt 17 is irrational, what can we conclude about the decimal expansion of sqrt 17 ?

Given that all mathematics textbooks are interesting, and suppose you are reading a mathematics textbook. What can we conclude about the textbook you are reading?

Use deductive reasoning to answer the following: Humans are mammals. All mammals are vertebrates. Based on these two statements, what can you conclude about humans?

Three students X,Y and Z performed an experiment for studying the variation of alternating currents with angular frequency in a series LCR-circuit and obtained the graphs shown in the figure They all used a.c sources of the same r.m.s. value and inductances of the same value. What can we conclude about the capacitance value. What can we conclude about nature of the impedance of the set up at frequency omega_0 ?

Given that sqrt p is irrational for all prime p and also suppose that 3721 is a prime. Can you conclude that sqrt 3721 is an irrational number ? Is your conclusion correct ? Why or why not ?

Three students X,Y and Z performed an experiment for studying the variation of alternating currents with angular frequency in a series LCR-circuit and obtained the graphs shown in the figure They all used a.c sources of the same r.m.s. value and inductances of the same value. What can we conclude about the resistance values used by them