T or F with explanation for each part please

Problem 1 (10 Marks) Use "T" or "F" to indicate if each of the following statements is True or False. Write the answers on your answering booklet. If necessary, make further assumptions. 1.1) Generally speaking, an integer programming (IP) problem is more difficult to solve if it has more integer variables. 1.2) Generally speaking, converting a general IP problem to a binary IP problem and then solving the binary IP problem will use less computing time comparing to solving the general IP problem directly 1.3) The multiplication of 1 binary variable and I general integer variable may be linearized by introducing an additional binary variable and several linear constraint functions. 1.4) The optimal objective function value of a minimization IP problem is always equal to or less than that of the corresponding relaxed LP problem. 1.5) An integer programming problem can be solved by solving the corresponding relaxed linear programming problem ifall coefficients and right hand sides of the constraint functions are integers