Use rules of inference and logical equivalences to show that the following arguments are valid. be sure to cite which rules of inference or logical equivalences you use on each line of your proof, and indicate which line numbers are involved in each step. (a) the argument has premises: -s, t1 → p, q → (u^ t), and (p^ t) → (b) the argument has premises: vz [e(z) → (plz)^-a(z))] and-3r (p(z)va(z)); and conclusion: (r v s), and conclusion: q → r -3r c(r)

Write a new lc-3 trap subroutine (i.e. a subroutine that will be invoked via the trap instruction) that will receive a numeric digit entered at the keyboard (i.e. an ascii character), echo it to the screen, and return in r0 the corresponding numeric value: so if the user types the digit '7', the character '7' will appear on the screen, but the value returned in r0 will be b0000 0000 0000 0111 (#7) you may not use any trap calls in your code - you must implement the "polling" code that interrogates the keyboard status and data registers. ; getnum_tsr ; a subroutine for obtaining a numeric value ; given ascii numeric digit input to keyboard. ; the numeric digit is echoed to the console (e.g. '7' = b0000 0000 0011 0111), ; but the value returned in r0 is the actual numeric value ; corresponding to the digit (e.g. b0000 0000 0000 0111 =