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  This is a 43-year-old female with history of infertility. The patient also complained constipation and increasing abdominal girth. An ultrasound study was performed. Most probably the abnormality is:

Image for questions  21-25 No 1 is pointing to:

  A 25-day postpartum woman complains of intense pelvic pain, fever and increased WBCC. What is the most likely diagnosis?

  A 55-years-old woman who underwent hysterectomy for endometrial cancer. The structure measured is:

A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refers to whether person x is an officer of the club. The predicate D(x) indicates whether person x has paid his or her club dues. The domain is the set of all members of the club. The names of the members and their truth values for each of the predicates is given in the following table. Indicate whether each expression is true or false. Name M(x) O(x) D(x) Hillary T F T Bernie F T F Donald F T F Jeb F T T Carly F T F   ∀x ¬(O(x) ↔ D(x))   [Q1] ∀x ((x ≠ Jeb) → ¬(O(x) ↔ D(x)))   [Q2] ∀x (¬O(x) → D(x))   [Q3] ∃x (M(x) ∧ D(x))   [Q4] ∃x (O(x) → M(x))   [Q5] ∃x (M(x) ∧ O(x) ∧ D(x))   [Q6]  

How many solutions are there to the equation  x1 + x2 + x3 + x4 + x5 + x6 = 37, where each xi is a non-negative integer?  

Consider the problem of purchasing cans of juice. Suppose that juice is sold in 2-packs or 5-packs. Let Q(n) be the statement that it is possible to buy n cans of juice by combining 2-packs and 5-packs. This problem discusses using strong induction to prove that for any n ≥ 4, Q(n) is true. 1) The inductive step will prove that for k ≥ 5, Q(k+1) is true. What is the inductive hypothesis? (a) Q(j) is true for any j = 4, 5, …, k. (b) Q(j) is true for any j = 4, 5, …, k+1. (c) Q(j) is true for any j = 5, …, k+1. [Q1]   2) The inductive step will prove that for k ≥ 5, Q(k+1) is true. What part of the inductive hypothesis is used in the proof? (a) Q(k-2) (b) Q(k-1) (c) Q(k) [Q2]   3)In the base case, for which values of n should Q(n) be proven directly? (a) n = 3, n = 4, and n = 5. (b) n = 4 and n = 5. (c) n = 4, n = 5, and n = 6. [Q3]

Determine the truth value of each expression below. The domain is the set of all real numbers. ∀x∃y (xy > 0)  [Q1] ∃x∀y (xy = 0)  [Q2] ∀x∀y∃z (z = (x – y)/3)  [Q3] ∀x∃y∀z (z = (x – y)/3)  [Q4] ∀x∃y y2 = x   [Q5] ∀x∃y (x < 0 ∨ y2 = x)   [Q6] ∃x ∃y (x2 = y2 ∧ x ≠ y)  [Q7] ∀x ∀y (x2 ≠ y2 ∨ |x| = |y|)   [Q8]

Indicate whether each of the following arguments is valid or invalid.   If is an irrational number, then    is an irrational number. is an irrational number.∴   is an irrational number.   [Q1] p ↔ qp ∨ q∴ p   [Q2] ¬(p → q)q → p∴ ¬q    [Q3] q → pp∴ ¬(p → q)    [Q4] The patient has high blood pressure or diabetes or both.The patient has diabetes or high cholesterol or both.∴ The patient has high blood pressure or high cholesterol.  [Q5] ∀x (P(x) → Q(x))∃x ¬P(x)∴ ∃x ¬Q(x)   [Q6]

How many vertices does a full 4-ary tree with 50 internal vertices have?