HSRT Deductive Reasoning Application 2 — Questions and Answers
Question 1: Premise 1: All patients with serum sodium below 125 mEq/L require urgent intervention. Premise 2: Mr. Ortega's serum sodium is 121 mEq/L. What follows deductively?
- Mr. Ortega requires urgent intervention (Correct answer)
- Mr. Ortega may require urgent intervention depending on his symptoms
- Mr. Ortega's sodium is critically low only if he is symptomatic
- Additional tests are needed before any conclusion can be drawn
Correct answer: Mr. Ortega requires urgent intervention
If all patients below 125 mEq/L require urgent intervention, and Mr. Ortega is below that threshold, deductive logic guarantees he requires urgent intervention.
This is a classic categorical syllogism (modus ponens structure): All A → B; X is A; therefore X → B. Given the universal premise and the specific fact, the conclusion is deductively certain — not probabilistic. In clinical contexts, deductive rules (protocols) are designed precisely to remove ambiguity. Symptoms may modify treatment urgency in practice, but the logical conclusion from the stated premises is unambiguous. Deductive validity means: if the premises are true, the conclusion must be true.
Question 2: A clinical protocol states: 'No patient on anticoagulation therapy should receive intramuscular injections.' The nurse knows that Mrs. Lee is on warfarin. What deductively follows?
- Mrs. Lee should not receive intramuscular injections (Correct answer)
- Mrs. Lee should receive subcutaneous injections instead, but only after consulting a physician
- The rule applies only to high-dose warfarin patients
- Mrs. Lee can receive IM injections if no other route is available
Correct answer: Mrs. Lee should not receive intramuscular injections
A universal prohibition applied to a specific case deductively yields a certain conclusion: Mrs. Lee should not receive IM injections.
Deductive reasoning from universal clinical rules to specific patients is the foundation of protocol-based care. If the premise 'No anticoagulated patient receives IM injections' is accepted as the rule, and Mrs. Lee is anticoagulated, the conclusion 'Mrs. Lee does not receive IM injections' follows with logical necessity. IM injections in anticoagulated patients risk hematoma formation. The deductive structure here is modus ponens. The other options introduce conditions or exceptions not stated in the premises, which would require new information.
Question 3: From the premises: 'All community-acquired pneumonias should be treated with empiric antibiotics within 4 hours of diagnosis' and 'Patient X was diagnosed with community-acquired pneumonia at 10:00 AM,' which deductive conclusion is valid?
- Patient X should receive empiric antibiotics no later than 2:00 PM (Correct answer)
- Patient X should receive empiric antibiotics if his oxygen saturation drops below 90%
- Patient X may wait for culture results before starting antibiotics
- Patient X requires antibiotics only if he is immunocompromised
Correct answer: Patient X should receive empiric antibiotics no later than 2:00 PM
Applying the universal rule to the specific patient: diagnosis at 10:00 AM + 4-hour window = treatment no later than 2:00 PM.
This deductive application involves substituting the specific fact (diagnosis at 10:00 AM) into the universal rule (treat within 4 hours). The conclusion is mathematically and logically certain: 10:00 + 4:00 = 14:00, so antibiotics must be given by 2:00 PM. The other options introduce conditions (O2 sat, cultures, immune status) not present in the premises, making them invalid deductive conclusions from the stated information. Deductive validity does not permit adding new conditions to the conclusion.
Question 4: A medical student is presented with the following argument: 'If a patient is in anaphylactic shock, epinephrine is indicated. This patient is not in anaphylactic shock. Therefore, epinephrine is not indicated.' Is this deductively valid?
- No — this is the fallacy of denying the antecedent; epinephrine may be indicated for other reasons (Correct answer)
- Yes — the argument correctly identifies when epinephrine is and is not needed
- Yes — the absence of anaphylaxis logically excludes all indications for epinephrine
- No — the argument contains a false premise about anaphylaxis treatment
Correct answer: No — this is the fallacy of denying the antecedent; epinephrine may be indicated for other reasons
Denying the antecedent (If P then Q; not P; therefore not Q) is an invalid deductive form. Epinephrine has other indications beyond anaphylaxis.
The argument follows the invalid form 'If P then Q; not P; therefore not Q,' known as denying the antecedent. The valid inference from 'If P then Q' combined with 'not P' is nothing — the conclusion about Q is indeterminate. Epinephrine is also indicated in cardiac arrest (ACLS protocols), severe asthma, croup, and other conditions. The only valid forms of hypothetical syllogism are modus ponens (affirming the antecedent) and modus tollens (denying the consequent).
Question 5: A physical therapist deduces: 'All patients with a Berg Balance Scale score below 45 are at high fall risk. Ms. Chen scored 38. Therefore Ms. Chen is at high fall risk.' This argument is BEST characterized as:
- Deductively valid — the conclusion follows necessarily from the premises if they are true (Correct answer)
- Inductively strong — the conclusion is probably true given the premises
- Invalid — the Berg Balance Scale is not a perfect predictor
- Circular — the conclusion restates one of the premises
Correct answer: Deductively valid — the conclusion follows necessarily from the premises if they are true
The argument is a valid categorical syllogism: universal rule + specific case = certain conclusion. Deductive validity depends on logical form, not on whether the premises are factually perfect.
Deductive validity means: if the premises are true, the conclusion must be true. The structure here is valid (universal affirmative + particular affirmative → particular affirmative). Whether the Berg Balance Scale is a perfect predictor in practice is a question of soundness (whether the premises are actually true), not validity (whether the form is correct). A valid argument with false premises is unsound but still logically valid. This distinction between validity and soundness is fundamental to deductive reasoning in health sciences.
Question 6: Premise: 'If a medication has a narrow therapeutic index, plasma level monitoring is required.' Medication Y has a narrow therapeutic index. A pharmacist concludes that plasma level monitoring is required for Medication Y. This inference is:
- Modus ponens — a valid deductive argument affirming the antecedent (Correct answer)
- Modus tollens — a valid deductive argument denying the consequent
- Affirming the consequent — an invalid deductive form
- Inductive generalization — a probable conclusion from observed cases
Correct answer: Modus ponens — a valid deductive argument affirming the antecedent
The form 'If P then Q; P; therefore Q' is modus ponens, the most fundamental valid deductive argument form.
Modus ponens: If P → Q, and P is true, then Q must be true. Here: P = 'drug has narrow therapeutic index'; Q = 'plasma monitoring required'; the pharmacist affirms P and concludes Q — this is modus ponens and is deductively valid. Modus tollens would deny Q to conclude not-P. Affirming the consequent (If P then Q; Q; therefore P) is the invalid converse error. Inductive generalization involves moving from specific observations to a general rule, which is not what occurs here.
HSRT Deductive Reasoning Application 2
Premise 1: All patients with serum sodium below 125 mEq/L require urgent intervention.
Premise 2: Mr.
Ortega's serum sodium is 121 mEq/L.
What follows deductively?