Outline a natural deduction proof that formalizes the conditional intro-duction and conditional elimination steps of the proof of lemma 3 below.
lemma 1.if x is a real number, then x−1 is a real number.
lemma 2. if y is a real number, then 0≤y2 .
lemma 3. if z is a real number, then2z≤z2+ 1.

20+ ! come and answer quick! triangle mno is reflected over the x-axis and then translated up 4 and right 3. how can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position? a translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis. b translate the pre-image up 3 and right 4 and then reflect the figure over the x-axis. c translate the pre-image up 4 and left 3 and then reflect the figure over the y-axis. d translate the pre-image down 3 and right 4 and then reflect the figure over the x-axis.

Solve this and show you’re work step by step ! -5 3/4+3h< 9 1/4 -

In the figure below, triangle rpq is similar to triangle rts. what is the distance between p and q? a. 24 b. 42 c.50 d. 54